•THERMODYNAMICS 


OF    THE 


STEAM-ENGINE 


AND   OTHER   HEAT-ENGINES. 


BY 


CECIL    H.    P^ABODY, 

PROFESSOR  OF  MARINE  ENGINBKRING  AND  NAVAL  ARCHITECTURE, 
MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY. 


FOURTH  EDITION,  REWRITTEN  AND  RESET. 
FIRST  THOUSAND. 


NEW  YORK: 

JOHN   WILEY  &  SONS. 
LONDON  :   CHAPMAN    &   HALL,   LIMITED 

1898. 


Engineering 
Library 


Copyright,  1898, 

BY 
CECIL   K.   PEABODY. 


74^631 


ROBERT    DRUMMOND,    PRINTER,    NEW    YORK. 


PREFACE. 


THIS  work  is  designed  to  give  instruction  to  students  in 
technical  schools  in  the  methods  and  results  of  the  application 
of  thermodynamics  to  engineering.  While  it  has  been  con- 
sidered desirable  to  follow  commonly  accepted  methods,  some 
parts  differ  from  other  text-books,  either  in  substance  or  in 
manner  of  presentation,  and  may  require  a  few  words  of 
explanation. 

The  general  theory  or  formal  presentation  of  thermody- 
namics is  that  employed  by  the  majority  of  writers,  and  was 
prepared  with  the  view  of  presenting  clearly  the  difficulties 
inherent  in  the  subject,  and  of  giving  familiarity  with  the 
processes  employed. 

In  the  discussion  of  the  properties  of  gases  and  vapors  the 
original  experimental  data  on  which  the  working  equations, 
whether  logical  or  empirical,  must  be  based  are  given  quite 
fully,  to  afford  an  idea  of  the  degree  of  accuracy  attainable  in 
calculations  made  with  their  aid.  Rowland's  determination 
of  the  mechanical  equivalent  of  heat  has  been  adopted,  and 
with  it  his  determination  of  the  specific  heat  of  water  at  low 
temperatures.  The  author's  "  Tables  of  the  Properties  of 
Saturated  Steam  and  Other  Vapors"  were  calculated  to 
accompany  this  work,  and  may  be  considered  to  be  an 
integral  part  of  it. 

The  chapters  on  the  flow  of  gases  and  vapors  and  on  the 
injector  are  believed  to  present  some  novel  features,  espe- 
cially in  the  comparisons  with  experiments. 

The  feature  in  which  this  book  differs  most  from  similar 
works  is  in  the  treatment  of  the  steam-engine.  It  has  been 
deemed  advisable  to  avoid  all  approximate  theories  based  on 

iii 


IV  PREFA  CE. 

the  assumption  of  adiabatic  changes  of  steam  in  an  engine 
cylinder,  and  instead  to  make  a  systematic  study  of  steam- 
engine  tests,  with  the  view  of  finding  what  is  actually  known 
on  the  subject,  and  how  future  investigations  and  improve- 
ments may  be  made.  For  this  purpose  a  large  number  of 
tests  have  been  collected,  arranged,  and  compared.  Special 
attention  is  given  to  the  investigations  of  the  action  of  steam 
in  the  cylinder  of  an  engine,  considerable  space  being  given 
to  Hirn's  researches  and  to  experiments  that  provide  the 
basis  for  them.  Directions  are  given  for  testing  engines,  and 
for  designing  simple  and  compound  engines. 

Chapters  have  been  added  on  compressed-air  and  refriger- 
ating machines,  to  provide  for  the  study  of  these  important 
subjects  in  connection  with  the  theory  of  thermodynamics. 

Wherever  direct  quotations  have  been  made,  references 
have  been  given  in  foot-notes,  to  aid  in  more  extended  in- 
vestigations. It  does  not  appear  necessary  to  add  other 
acknowledgment  of  assistance  from  well-known  authors, 
further  than  to  say  that  their  writings  have  been  diligently 
searched  in  the  preparation  of  this  book,  since  any  text-book 
must  be  largely  an  adaptation  of  their  work  to  the  needs  of 
instruction. 

C.  H.  P. 

MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY, 
May,   1889. 


PREFACE  TO   FOURTH   EDITION. 


A  THOROUGH  revision  of  this  work  has  been  made  to 
bring  it  into  accord  with  more  recent  practice  and  to  include 
later  experimental  work.  Advantage  is  taken  of  this  oppor- 
tunity to  make  changes  in  matter  or  in  arrangement  which  it 
is  believed  will  make  it  more  useful  as  a  text-book. 

C.  H.  P. 

MASSACHUSETTS  INSTITUTE  OF  TECHNOLOGY. 
July,  i8ga 


TABLE  OF  CONTENTS. 


CHAPTER  ,  PAGE 

I.  THERMAL  CAPACITIES i 

II.  FIRST  LAW  OF  THERMODYNAMICS 15 

III.  SECOND  LAW  OF  THERMODYNAMICS 25 

IV.  FUNDAMENTAL  EQUATIONS 44 

V.  PERFECT  GASES 54 

VI.  SATURATED  VAPORS 80 

VII.  SUPERHEATED  VAPORS 123 

VIII.  FLOW  OF  FLUIDS 149 

IX.  INJECTORS 163 

X.  HOT-AIR  ENGINES  AND  GAS-ENGINES 194 

XI.  THE  STEAM-ENGINE 229 

XII.  COMPOUND-ENGINES 255 

XIII.  TESTING  STEAM-ENGINES 280 

XIV.  INFLUENCE  OF  THE  CYLINDER-WALLS 301 

XV.  ECONOMY  OF  STEAM-ENGINES 353 

XVI.  FRICTION  OF  ENGINES 429 

XVII.  COMPRESSED  AIR 442 

XVIII.  REFRIGERATING  MACHINES , 479 

v 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


CHAPTER  I. 
THERMAL  CAPACITIES. 

THE  object  of  thermodynamics,  or  the  mechanical  theory 
of  heat,  is  the  solution  of  problems  involving  the  action  of 
heat,  and,  for  the  engineer,  more  especially  those  problems 
presented  by  the  steam-engine  and  other  thermal  motors.  In 
this  work  the  discussion  of  the  actual  nature  of  heat  and  the 
rationale  of  its  various  actions  will  be  purposely  avoided,  and 
attention  will  be  given  rather  to  the  calculation  of  the  results 
of  such  actions. 

Effects  of  Heat. — In  general  the  action  of  heat  on  a 
given  substance  changes  all  the  characteristics  of  that  sub- 
stance, such  as  density,  temperature,  elasticity,  conductivity, 
etc.  A  comprehensive  theory  of  thermodynamics  should 
make  it  possible  to  calculate  such  changes  in  any  of  the  char- 
acteristics of  any  substance.  In  fact,  the  number  of  substances 
for  which  we  have  adequate  theoretical  and  experimental 
knowledge  is  limited,  and  only  a  few  characteristics  of  such 
substances  are  commonly  included  in  our  discussions. 

The  substances  in  which  the  engineer  has  the  most  interest 
are  gases  and  vapors,  more  especially  air  and  steam.  Fortu- 
nately an  adequate  treatment  can  be  given  of  these  substances 
for  engineering  purposes. 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

First  General  Principle. — In  the  development  of  the 
theory  of  thermodynamics  it  is  assumed  that  if  any  two 
characteristics  or  properties  of  a  substance  are  known  these 
two,  treated  as  independent  variables,  will  enable  us  to  calcu- 
late any  third  property. 

As  an  example  we  have  from  the  combination  of  the  laws 
*of  Boyle  and  Gay-Lussac  the  general  equation  for  gases. 


in  which  /  is  the  pressure,  v  is  the  volume,  T  is  the  absolute 
temperature  by  the  air-thermometer,  and  R  is  a  constant 
which  for  air  has  the  value  53.22  when  English  units  are 
used.  It  is  probable  that  this  equation  led  to  the  general 
assumption  just  quoted.  That  assumption  is  purely  arbitrary, 
and  is  to  be  justified  by  its  results.  It  may  properly  be  con- 
sidered to  be  the  first  general  principle  of  the  theory  of  ther- 
modynamics; the  other  two  general  principles  are  the  so- 
called  first  and  second  laws  of  thermodynamics,  which  will  be 
stated  and  discussed  later. 

Characteristic  Equation. — An  equation  which  gives  the 
relations  of  the  properties  of  any  substance  is  called  the 
characteristic  equation  for  that  substance.  The  properties 
appearing  in  a  characteristic  equation  are  commonly  pressure, 
volume,  and  temperature,  but  other  properties  may  be  used 
if  convenient.  The  form  of  the  equation  must  be  determined 
from  experiments,  either  directly  or  indirectly. 

The  characteristic  equation  for  a  gas  is,  as  already  quoted, 

pv  =  RT, 
which  may  be  written  also 

RT  RT 

p=       — ,         v  — — ,         pv 

A  similar  treatment  may  be  applied  to  any  characteristic 


THERMAL    CAPACITIES,  3 

equation  in  terms  of  pressure,  volume,   and  temperature,   so 
that  we  may  have 

T  =  F(p,  v\         p  -  F>(T,  v),         v  =  F,(T,  /), 

or  in  general 

f(p,v,  T)  =  o .     (2) 

If  x,  y,  and  z  represent  any  properties  or  characteristics  of 
a  substance,  then  the  first  general  principle  may  be  expressed 
algebraically  by 

/(*,  y,  z)  =  o.     .     .     '.     .     .     .     (3) 

Specific  Pressure. — The  pressure  is  assumed  to  be  a 
hydrostatic  pressure,  such  as  a  fluid  exerts  on  the  sides  of  the 
containing  vessel  or  on  an  immersed  body.  The  pressure  is 
consequently  the  pressure  exerted  by  the  substance  under  con- 
sideration rather  than  the  pressure  on  that  substance.  For 
example,  in  the  cylinder  of  a  steam-engine  the  pressure  of  the 
steam  is  exerted  on  the  piston  during  the  forward  stroke  and 
does  work  on  the  piston;  during  the  return  stroke,  when  the 
steam  is  expelled  from  the  cylinder,  it  still  exerts  pressure  on 
the  piston  and  abstracts  work  from  it. 

For  the  purposes  of  the  general  theory  pressures  are 
expressed  in  terms  of  pounds  on  the  square  foot  for  the 
English  system  of  units.  In  the  metric  system  the  pressure  is 
expressed  in  terms  of  kilograms  on  the  square  metre.  A 
pressure  thus  expressed  is  called  the  specific  pressure.  In 
engineering  practice  other  terms  are  used,  such  as  pounds  on 
the  square  inch,  inches  of  mercury,  millimetres  of  mercury, 
atmospheres,  or  kilograms  on  the  square  centimetre. 

Specific  Volume. — It  is  convenient  to  deal  with  one  unit 
of  weight  of  the  substance  under  discussion,  and  to  consider 
the  volume  occupied  by  one  pound  or  one  kilogram  of  the 
substance ;  this  is  called  the  specific  volume ',  and  is  expressed 
in  cubic  feet  or  in  cubic  metres.  The  specific  volume  of  air 


4  THERMODYNAMICS   CF   THE   STEAM-ENGINE. 

at  freezing-point  and  under  the  normal  atmospheric  pressure 
is  12.39  cubic  feet;  the  specific  volume  of  saturated  steam  at 
212°  F.  is  26.6  cubic  feet;  and  the  specific  volume  of  water 

is  about  ,  or  nearly  0.016  of  a  cubic  foot. 

62.4 

Temperature  is  commonly  measured  by  aid  of  a  mercurial 
thermometer  which  has  for  its  reference-points  the  freezing- 
point  and  boiling-point  of  water.  A  centigrade  thermometer 
has  the  volume  of  the  stem  between  the  reference-points 
divided  into  one  hundred  equal  parts  called  degrees.  The 
Fahrenheit  thermometer  differs  from  the  centigrade  in  having 
one  hundred  and  eighty  degrees  between  the  freezing-point 
and  the  boiling-point,  and  in  having  its  zero  thirty-two  degrees 
below  freezing. 

The  scale  of  a  mercurial  thermometer  is  entirely  arbitrary, 
and  its  indications  depend  on  the  relative  expansion  of  glass 
and  mercury.  Indications  of  such  thermometers,  however 
carefully  made,  differ  appreciably,  mainly  on  account  of  the 
varying  nature  of  the  glass.  For  refined  investigations  ther- 
mometric  readings  are  reduced  to  the  air-thermometer,  which 
has  the  advantage  that  the  expansion  of  air  is  so  large  com- 
pared with  the  expansion  of  glass  that  the  latter  has  little  or 
no  effect. 

It  is  convenient  in  making  calculations  of  the  properties  of 
air  to  refer  temperatures  to  the  absolute  zero  of  the  scale 
of  the  air-thermometer.  To  get  a  conception  of  what  is 
meant  by  this  expression  we  may  imagine  the  air-thermom- 
eter to  be  made  of  a  uniform  glass  tube  with  a  proper 
index  to  show  the  volume  of  the  air.  The  position  of 
the  index  may  be  marked  at  boiling-point  and  at  freez- 
ing-point as  on  the  mercurial  thermometer,  and  the  space 
between  may  be  divided  into  one  hundred  parts  or  degrees. 
If  the  graduations  are  continued  to  the  closed  end  of  the 
tube  there  will  be  found  to  be  between  273  and  274  of 
them.  It  will  be  shown  later  that  there  is  reason  to  suppose 
that  the  absolute  zero  of  temperature  is  273.7  degrees  centi- 


7  HER  MA  L    CAPA  Cf  TIES.  5 

grade  below  the  freezing-point  of  water.  Speculations  as  to 
the  meaning  of  absolute  zero  and  discussions  concerning  the 
nature  of  substances  at  that  temperature  are  not  now  profit- 
able. It  is  sufficient  to  know  that  equations  are  simplified 
and  calculations  are  facilitated  by  this  device.  For  example, 
if  temperature  is  reckoned  from  the  arbitrary  zero  of  the 
centigrade  thermometer,  then  the  characteristic  equation  for  a 
perfect  gas  becomes 


in    which   a   is   the   coefficient   of   dilatation   and  -  =   273.7 

nearly. 

In  order  to  distinguish  the  absolute  temperature  from  the 
temperature  by  the  thermometer  we  shall  designate  the 
former  by  T  and  the  latter  by  /,  bearing  in  mind  that 

T  =  /  +  273.7°  centigrade, 
T  =  t  +  460.7°  Fahrenheit. 

It  will  appear  in  the  course  of  the  development  of  the 
theory  of  thermodynamics  that  a  scale  of  temperature  can  be 
constructed  depending  on  the  fundamental  units  of  length  and 
weight,  such  as  the  foot  and  the  pound.  Such  a  scale  is 
properly  called  the  absolute  scale  of  temperature,  because  it 
does  not  depend  on  the  properties  of  any  substance  (glass, 
mercury,  or  air),  and  because  degrees  may  be  given  the  same 
value  or  significance  in  all  parts  of  the  scale.  That  a  degree 
on  the  air-thermometer  has  not  the  same  value  in  all  parts  of 
the  scale  is  shown  by  the  fact  that  the  scale  of  the  air-ther- 
mometer differs  slightly  from  that  of  the  absolute  thermom- 
eter, as  will  be  seen  from  the  table  on  page  73.  The  irregu- 
larities of  the  scale  of  a  mercurial  thermometer  are  much 
greater,  so  that  physical  observations  are  reduced  to  the  scale 
of  the  air-thermometer-,  in  engineering  tests  it  is  usually  sufifi- 


THERMODYNAMICS   OF   THE  STEAM-ENGINE. 


cient  to  take  the  readings  of  the  mercurial  thermometer  with- 
out such  a  reduction. 

In  the  development  of  the  theory  of  thermodynamics  it  will 
be  assumed  that  temperatures  are  referred  to  the  absolute  scale, 
though  as  yet  we  do  not  know  the  nature  of  that  scale  or  how 
it  is  constructed.  The  apparent  indefmiteness  accompanying 
this  suspension  of  judgment  is  much  more  than  compensated 
for  by  the  ease  with  which  the  absolute  scale  can  be  defined 
when  we  arrive  at  the  proper  place  for  doing  so. 

Graphical  Representation  of  the  Characteristic  Equa- 
tion.— Any  equation  with  three  variables  may  be  represented 
by  a  geometrical  surface  referred  to  coordinate  axes,  of  which 
surface  the  variables  are  the  coordinates.  In  the  case  of 
a  perfect  gas  which  conforms  to  the  equation 

pv  =  RT 

the  surface  is  such  that  each  section  perpendicular  to  the  axis 
of  T is  a  rectangular  hyperbola  (Fig.  i). 
Returning  now  to  the  general  case, 
it  is  apparent  that  the  characteristic 
equation  of  any  substance  may  be 
represented  by  a  geometrical  surface 
referred  to  coordinate  axes,  since  the 
equation  is  assumed  to  contain  only 
three  variables;  but  the  surface  will  in 
general  be  less  simple  in  form  than  that 
representing  the  combined  laws  of  Boyle  and  Gay-Lussac. 

If  one  of  the  variables,  as  7",  is  given  a  special  constant 
value  it  is  equivalent  to  taking  a  section  perpendicular  to  the 
axis  of  T]  and  a  plane  curve  will  be  cut  From  the  surface, 
which  may  be  conveniently  projected  on  the  (/>,  v)  plane. 
The  reason  for  choosing  the  (/,  v)  plane  is  that  the  curves 
correspond  with  those  drawn  by  the  steam-engine  indicator. 

Considerable  use  is  made  of  such  thermal  curves  in  explain- 
ing thermodynamic  conceptions.  As  a  rule,  a  graphical  proc- 


FIG.    i. 


THERMAL    CAPACITIES.  7 

ess  or  representation  is  merely  another  way  of  presenting  an 
idea  that  has  been,  or  may  be,  presented  analytically;  there 
is,  however,  an  advantage  in  representing  a  condition  or 
a  change  to  the  eye  by  a  diagram,  especially  in  a  discussion 
which  appears  to  be  abstract.  A  number  of  thermal  curves 
are  explained  on  page  18. 

Standard  Temperature. — For  many  purposes  it  is  con- 
venient to  take  the  freezing-point  of  water  for  the  standard 
temperature,  since  it  is  one  of  the  reference-points  on  the 
thermometric  scale;  this  is  especially  true  for  air.  But  the 
properties  of  water  change  rapidly  at  and  near  freezing-point 
and  are  very  imperfectly  known.  It  has  consequently  become 
customary  to  take  62°  F.  for  the  standard  temperature  for  the 
English  system  of  units;  there  is  a  convenience  in  this, 
inasmuch  as  the  pound  and  yard  are  standards  at  that  tempera- 
ture. For  the  metric  system  15°  C.  is  used,  though  the  kilo- 
gram and  metre  are  standards  at  freezing-point. 

Thermal  Unit. —  Heat  is  measured  in  calories  or  in  British 
thermal  units  (B.  T.  u.).  A  British  thermal  unit  is  the  heat 
required  to  raise  one  pound  of  water  from  62°  F.  to  63°  F.  ; 
in  like  manner  a  calorie  is  the  heat  required  to  raise  one  kilo- 
gram of  water  from  15°  C.  to  16°  C. 

The  calorie  is  often  defined  as  the  heat  required  to  raise  a 
kilogram  of  water  from  freezing-point  to  one  degree  centigrade ; 
and  a  B.  T.  U.  is  correspondingly  defined  as  the  heat  required 
to  raise  one  pound  of  water  from  freezing-point  to  33°  F.  The 
objection  to  the  use  of  the  freezing-point  as  the  standard  tem- 
perature— namely,  the  uncertainty  as  to  the  properties  of  water 
at  that  temperature — applies  even  more  forcibly  here.  The 
whole  subject  will  be  discussed  later  in  connection  with  Row- 
land's determination  of  the  mechanical  equivalent  of  heat. 

The  thermal  unit,  or  the  calorie,  should  depend  on  the 
absolute  scale  of  temperature,  but  for  practical  purposes  the 
scale  of  the  air-thermometer  is  sufficient. 

Thermal  Capacities. — The  amount  of  heat  required  to 
change  by  unity  any  quality  of  a  unit  of  weight  of  a  substance 


8  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

is  called  the  thermal  capacity  corresponding  to  the  given 
change. 

Three  thermal  capacities  have  received  names,  i.  e.,  specific 
heat  at  constant  volume,  specific  heat  at  constant  pressure, 
and  latent  heat  of  expansion. 

Specific  Heat  is  the  number  of  thermal  units  required  to 
raise  a  unit  of  weight  of  a  given  substance  one  degree  of 
temperature.  The  specif  c  heat  of  water  at  the  standard  tem- 
perature is,  of  course,  unity. 

If  the  specific  heat  of  a  given  substance  is  constant,  then 
the  heat  required  to  raise  one  pound  through  a  given  range  of 
temperature  is  the  product  of  the  specific  heat  by  the  increase 
of  temperature.  Thus  if  c  is  the  specific  heat  and  t  —  tl  is  the 
range  of  temperature  the  heat  required  is 

Q=c(t-  /,),  and  c  =  ~~  • 

If  the  specific  heat  varies  the  amount  of  heat  must  be 
obtained  by  integration  —  that  is, 


and  conversely 


It  is  customary  to  distinguish  two  specific  heats  for  perfect 
gases;  specific  heat  at  constant  pressure  and  specific  heat  at 
constant  volume,  which  may  be  represented  by 


The    subscript    attached    to    the     parenthesis   indicates  the 
property  which  is  constant  during  the  change. 

It  is  evident  that  the  specific  heats   just    expressed   are 
partial  differential  coefficients.      Partial  differentials  may  often 


THERMAL    CAPACITIES.  Q 

be  recognized  by  their  positions  in  equations  or  by  the  con- 
text. Sometimes  they  are  indicated  by  parentheses,  as 
above,  but  without  the  subscripts  ;  or  they  may  be  indicated 
by  a  special  type,  as 

dQ 


In  thermodynamics  several  variables  are  often  intro- 
duced, each  of  which  may  be  a  function  of  two  independent 
variables;  it  is  consequently  convenient,  if  not  essential,  to 
indicate  a  partial  differential  by  a  parenthesis  and  a  subscript, 
as  above. 

Latent  Heat  of  Expansion  is  the  amount  of  heat 
required  to  increase  the  volume  of  a  unit  of  weight  of  the 
substance  by  one  cubic  foot,  or  one  cubic  metre,  at  constant 
temperature.  It  may  be  represented  by 


General  Equations  of  the  Effects  Produced  by  Heat  — 

In  conformity  with  the  first  general  principle  the  heat  required 
to  produce  a  change  in  a  unit  of  weight  of  a  given  substance 
may  be  expressed  as  a  function  of  any  two  properties  of  the 
substance  ;  thus  we  may  have 


Q  =  p^t,  v),   Q  —  F2(t,p},  or  Q  =  F3(/,  v),       .     (4) 
Differentiating  the  several  equations  (4),  we  have 

» (s«) 


IO  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 


In  equation  (5#)  the  partial  differential  coefficients    "jT 


I  —  \   are  tne  specific  heat   at  constant  volume  and  the 
\dv)t 

latent  heat  of  expansion  ;  they  may  be   replaced  by  ^»and  /, 
giving 

v  ......      (5) 


,\ 
In  like  manner  the  differential  coefficient    r-jr  )    in    equa- 

tion (6a)  may  be  replaced  by  cp.     The  differential  coefficient 

{—  -)  is  also  a  thermal  capacity,  and  represents  the  amount 
\dp  It 

of  heat  that  must  be  added  to  increase  the  pressure  to  the 
extent  of  one  pound  per  square  foot  (or  one  kilogram  per 
square  metre).  No  name  has  been  given  to  this  thermal 
capacity  ;  it  may  be  represented  by  the  letter  w,  and  equation 
(6a)  becomes 

dQ  =  cjdt  +  mdp.       .     .     .      .      .      (6) 

Finally,  I—  \  may  be  represented  by  n,  and  (~\  by  oy 

\dp]v  \av)p 

both  being  thermal  capacities  without  names,  and  equation 
(Jo)  becomes 

dQ  —  ndp  +  odv  .......      (7) 

Relations  of  the  Thermal  Capacities.  —  The  three  equa- 
tions (5),  (6),  and  (7)  show  the  changes  produced  by  the 
addition  of  an  amount  of  heat  dQ  to  a  unit  of  weight  of  a 
substance,  the  difference  coming  from  the  methods  of  analyz- 
ing the  changes.  We  may  conveniently  find  the  relations  of 
the  several  thermal  capacities  by  the  method  of  undetermined 
coefficients.  Thus  equating  the  right-hand  members  of  equa- 
tions (5)  and  (6), 

cvdt  +  Idv  =  cpdt  +  mdp.      .      .      .      .     (8) 


THERMAL    CAPACITIES.  II 

From  the  first  general  principle  we  have 


from  which,  by  differentiating  we  have 

dv  =  (d2\dt+(d^\ 
\dt)t          \dp)t 

which  substituted  in  (8)  gives 


(9) 


It  will  be  noted  that,  as  T  differs  from  t  only  by  the  addi- 
tion of  a  constant,  the  differential  dt  may  be  used  in  all  cases, 
whether  we  are  dealing  with  absolute  temperatures  or  temper- 
atures on  the  ordinary  thermometer. 

In  equation  (9)  p  and  T  are  independent  variables,  and 
each  may  have  all  possible  values;  consequently  we  may 
equate  like  coefficients. 

'   '   '   '   <"> 


Again,  equating  the  remaining  coefficients, 

lld^\  =  m.       ,     ..<.     .     .  (12) 

\dPh 

Again,  we  have 

p  =  F,(T,  v), 
from  which 


12  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

which  substituted  in  (8)  gives 


Equating  like  coefficients, 

e,  ......     (14) 


or 

^/>. 

--c>-c, (IS) 


From  equations  (6)  and  (7) 

Cpdt  -f-  mdp  =  ndp  -f-  odv (16) 

And  from  the  equation 


we  have 


•*=(S*+  ($).*• 

which  substituted  in  equation  (16)  gives 

ct(~T~\  dv  +  cp[—\  dp  4-  mdp  =  ndp  -f-  odv. 
\dv)p  \dp)v 


Equating  coefficients  of  dv, 


Finally,  from  equations  (5)  and  (7)  we  have 
cvdt  -(-  Idv  =  « 


THERM  A  L  .  CA  PA  CJ  TIES.  1 3 

Substituting  for  the  value  of  dt,  as  above, 

+ ^ = ndp + 

Equating  coefficients  of  dp, 


For  convenience  the  several  relations  of  the  thermal  ca- 
pacities may  now  be  assembled  as  follows : 


p 

dt 


idt\ 

"=<•(#). 


idi 

m  = 


='(); 


They  are  the  necessary  algebraic  relations  of  the  literal 
functions  growing  out  of  the  first  general  principle,  and  are 
independent  of  the  scale  of  temperature,  or  of  any  other  theo- 
retical or  experimental  principle  of  thermodynamics  other 
than  the  one  already  stated  —  namely,  that  any  two  properties 
of  a  given  substance,  treated  as  independent  variables,  are 
sufficient  to  allow  us  to  calculate  any  third  property. 

Of  the  six  thermal  capacities  the  specific  heat  at  constant 
pressure  is  the  only  one  that  is  commonly  known  by  direct 
experiment.  For  perfect  gases  this  thermal  capacity  is  a  con- 
stant, and,  further,  the  ratio  of  the  specific  heats 


is  a  constant,  so  that  cvis  readily  calculated.  The  relations  of 
the  thermal  capacities  allow  us  to  calculate  values  for  the 
other  thermal  capacities,  /,  m,  n,  and  o,  provided  that  we  can 


14  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

first  determine  the  several  partial  differential  coefficients  which 
appear  in  the  proper  equations.  But  for  a  perfect  gas  the 
characteristic  equation  is 


,     .     .     .     .     .     (19) 
from  which  we  have 

R 


.....       (20) 
\dl  Ip       p 

consequently 

/=!(<,-«;) (") 

so  that  /  may  be  readily  calculated  for  any  pressure.  Other 
partial  differential  coefficients  can  be  deduced  and  substituted, 
if  desired,  to  provide  means  of  calculating  the  other  thermal 
capacities ,  but  that  properly  belongs  in  the  discussion  of 
perfect  gases  and  will  be  considered  in  the  proper  place. 

For  a  different  substance — for  example,  superheated  steam 
— it  will  appear  that  the  ratio  of  the  specific  heats  is  not  a  con- 
stant, and,  further,  the  form  of  the  characteristic  equation  is 
different.  The  values  of  the  partial  differential  coefficients 
must  of  course  be  found  for  each  special  case,  and  the  use  to  be 
made  of  the  relations  of  the  thermal  capacities  will  depend 
on  circumstances. 


CHAPTER  II. 
FIRST    LAW   OF   THERMODYNAMICS. 

THE  formal  statement  of  the  first  law  of  thermodynamics  is : 

Heat  and  mechanical  energy  are  mutually  convertible^  and 
heat  requires  for  its  production  and  produces  by  its  disappearance 
a  definite  number  of  units  of  work  for  each  thermal  unit. 

This  law,  which  may  be  considered  to  be  the  second  gen- 
eral principle  of  thermodynamics,  is  the  statement  of  a  well- 
determined  physical  fact.  It  is  a  special  statement  of  the 
general  law  of  the  conservation  of  energy,  i.  e.,  that  energy 
may  be  transformed  from  one  form  to  another,  but  can  neither 
be  created  nor  destroyed.  It  should  be  stated,  however,  that 
the  general  law  of  conservation  of  energy,  though  universally 
accepted,  has  not  been  proved  by  direct  experiment  in  all 
cases ;  there  may  be  cases  that  are  not  susceptible  of  so  direct 
a  proof  as  we  have  for  the  transformation  of  heat  into  work. 

The  best  determinations  of  the  mechanical  equivalent  of 
heat  were  made  by  Rowland,  whose  work  will  be  considered 
in  detail  in  connection  with  the  properties  of  steam  and  water. 
From  his  work  it  appears  that  778  foot-pounds  of  work  are 
required  to  raise  one  pound  of  water  from  62°  to  63°  Fahren- 
heit ;  this  value  of  the  mechanical  equivalent  of  heat  is  now 
commonly  accepted  by  engineers,  and  is  verified  by  the  latest 
determinations  by  Joule  and  other  experimenters. 

The  values  of  the  mechanical  equivalent  of  heat  for  the 
English  system  and  for  the  metric  system  are : 

I  B.  T.  u.  =  778  foot-pounds. 

i  calorie    =  426.9  metre-kilograms. 

15 


1 6  THERMODYNAMICS    OF    THE   STEAM-ENGINE. 

This  physical  constant  is  commonly  represented  by  the  letter 
J\  the  reciprocal  is  represented  by  A. 

In  older  works  on  thermodynamics  the  values  of  J  are  com- 
monly quoted  as  772  for  the  English  system  and  424  for  the 
metric  system.  The  error  of  these  values  is  about  one  per  cent. 

Effects  of  the  Transfer  of  Heat. — Let  a  quantity  of 
any  substance  of  which  the  weight  is  one  unit — i.  e.,  one  pound 
or  one  kilogram — receive  a  quantity  of  heat  dQ.  It  will,  in 
general,  experience  three  changes,  each  requiring  an  expendi- 
ture of  energy.  They  are  :  (i)  The  temperature  will  be  raised, 
and,  according  to  the  theory  that  sensible  heat  is  due  to  the 
vibrations  of  the  particles  of  the  body,  the  kinetic  energy  will  be 
increased.  Let  dS  represent  this  change  of  sensible  heat  or 
vibration  work  expressed  in  units  of  work.  (2)  The  mean 
positions  of  the  particles  will  be  changed  ;  in  general  the  body 
will  expand.  Let  dl  represent  the  units  of  work  required 
for  this  change  of  internal  potential  energy,  or  work  of  disgre- 
gation.  (3)  The  expansion  indicated  in  (2)  is  generally  against 
an  external  pressure,  and  to  overcome  the  same — that  is,  for 
the  change  in  external  potential  energy — there  will  be  required 
the  work  dW. 

If  during  the  transmission  no  heat  is  lost,  and  if  no  heat  !s 
transformed  into  other  forms  of  energy,  such  as  sound,  elec- 
tricity, etc.,  then  the  first  law  of  thermodynamics  gives 

dQ  =  A(dS  +  dl  +  dW) (22) 

It  is  to  be  understood  that  any  or  all  of  the  terms  of  the 
equation  may  become  zero  or  may  be  negative.  If  all  the 
terms  become  negative  heat  is  withdrawn  instead  of  added, 
and  dQ  is  negative.  It  is  not  easy  to  distinguish  between  the 
vibration  work  and  the  disgregation  work,  and  for  many  pur- 
poses it  is  unnecessary ;  consequently  they  are  treated  together 
under  the  name  of  intrinsic  energy,  and  we  have 

.       .       (23) 


FIRST  LAW  OF   THERMODYNAMICS.  I/ 

The  inner  work,  or  intrinsic  energy,  depends  on  the  state  of 
the  body,  and  not  at  all  on  the  manner  by  which  it  arrived  at 
that  state  ;  just  as  the  total  energy  of  a  falling  body,  with  refer- 
ence to  a  given  plane  consisting  of  kinetic  energy  and  potential 
energy,  depends  on  the  velocity  of  the  body  and  the  height 
above  the  plane,  and  not  on  the  previous  history  of  the  body. 

The  external  work  is  assumed  to  be  done  by  a  fluid 
pressure  ;  consequently 

dW  =  pdv,     ........      (24) 

p<*»>  .......  (25) 

where  z>,  and  v^  are  the  final  and  initial  volumes. 

In  order  to  find  the  value  of  the  integral  v  in  equation  (25) 
it  is  necessary  to  know  the  manner  in  which  the  pressure  varies 
with  the  volume.  Since  the  pressure  may  vary  in  different 
ways,  the  external  work  cannot  be  determined  from  the  initial 
and  final  states  of  the  body  ;  consequently  the  heat  required 
to  effect  a  change  from  one  state  to  another  depends  on  the 
manner  in  which  the  change  is  effected. 

Assuming  the  law  of  the  variation  of  the  pressure  and 
volume  to  be  known,  we  may  integrate  thus: 


(26) 


In  order  to  determine  E  for  any  state  of  a  body  it  would 
be  necessary  to  deprive  it  entirely  of  vibration  and  disgregation 
energy,  which  would  of  course  involve  reducing  it  to  a  state 
of  absolute  cold  ;  consequently  the  direct  determination  is 
impossible.  However,  in  all  our  work  the  substances  operated 
on  are  changed  from  one  state  to  another,  and  in  each  state 
the  intrinsic  energy  depends  on  the  state  only  ;  consequently 
the  change  of  intrinsic  energy  may  be  determined  from  the 
initial  and  final  states  only,  without  knowing  the  manner 
of  change  from  one  to  the  other. 


i8 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


All  succeeding  equations  will  be  arranged  to  involve  differ- 
ences of  energy  only,  and  the  hypothesis  involved  in  a  separa- 
tion into  vibration  and  disgregation  work  avoided. 

Thermal  Lines. — The  external  work  can  be  determined 
only  when  the  relations  of  /  and  v  are  known,  or,  in  general, 
when  the  characteristic  equation  is  known.  It  has  already  been 
shown  that  in  such  case  the  equation  may  be  represented  by  a 
geometrical  surface,  on  which  so-called  thermal  lines  can  be 
drawn  representing  the  properties  of  the  substance  under  con- 
sideration. These  lines  are  commonly  projected  on  the  (/,  v) 
plane.  It  is  convenient  in  many  cases  to  find  the  relation  of/ 
and  v  under  a  given  condition  and  represent  it  by  a  curve  drawn 
directly  on  the  (/,  v)  plane. 

Lines  of  Equal  Pressure. — The  change  of 
condition  takes  place  at  constant  pressure,  and 
consists  of  a  change  of  volume,  as  represented  in 
Fig.  2.  The  tracing-point  moves  from  a^  to  a^ 
and  the  volume  changes  from  v^  to  v9.  The 
work  done  is  represented  by  the  rectangular  area 


FIG.  2. 
under  a 


or  by 


W  = 


During  the  change  the  temperature  may  or  may  not  change ; 
the  diagram  shows  nothing  concerning  it. 

Lines  of  Equal  Volume. — The  pressure  in- 
creases at  constant  volume,  and  the  tracing-point 
moves  from  a^  to  <2a.  The  temperature  usually 
increases  meanwhile.  Since  dv  is  zero, 


W  = 


=  o. 


FIG.  3. 


Isothermal  Lines  or  Lines,  of  Equal  Temperature. 

The  temperature  remains  constant,  and  a  line  is  drawn,  usually 
convex,  toward  the  axis  OV.     The  pressure  of  a  mixture  of  a 


FIRST  LAW  OF   THERMODYNAMICS.  ig 

liquid  and  its  vapors  is  constant  for  a  given  temperature  ;  con- 
sequently the  isothermal  for  such  a  mixture  is  a  line  of  equal 
pressure,  represented  by  Fig.  2.  The  iso- 
thermal  of  a  perfect  gas,  on  the  other  hand,  is 
an  equilateral  hyperbola,  as  appears  from  the 
law  of  Boyle,  which  may  be  written 

pv  =  C.      .......      (27)  FIG.  4. 

Isodynamic  or  Isoenergic  Lines  are  lines  representing 
changes  during  which  the  intrinsic  energy  remains  constant. 
Consequently  all  the  heat  received  is  transformed  into  external 
work.  It  will  be  seen  later  that  the  isodynamic  and  isothermal 
lines  for  a  gas  are  the  same. 

Adiabatic  Lines.  —  A  very  important  problem  in  thermo- 
dynamics is  to  determine  the  behavior  of  a  substance  when 
a  change  of  condition  takes  place  in  a  non-conducting  vessel. 
During  the  change  —  for  example,  an  increase  of  volume  or  ex- 
pansion —  some  of  the  heat  in  the  substance  may  be  changed 
into  work;  but  no  heat  is  transferred  to  or  from  the  sub- 
stance through  the  walls  of  the  containing  vessel.  Such 
•changes  are  called  adikbatic  or  isoentropic  changes. 

Very  rapid  changes  of  dry  air  in  the  cylinder  of  an  air- 
compressor  or  a  compressed-air  engine  are  very  nearly  adi- 
abatic.  Adiabatic  changes  never  occur  in  the  cylinder  of  a 
steam-engine  on  account  of  the  rapidity  with  which  steam  is 
condensed  on  or  vaporized  from  the  cast-iron  walls  of  the 
cylinder. 

Since  there  is  no  transmission  of  heat  to  (or  from)  the 
working  substance,  equation  (26)  becomes 


=  A(E.-El 


OF   TUK 

UNIVERSITY 


20  THERMODYNAMICS    OF   THE   STEAM-ENGINE. 

that  is,  the  external  work  is  done  wholly  at  the  expense  of 
the  intrinsic  energy  of  the  working  substance,  as  must  be  the 
case  in  conformity  with  the  assumption  of  an  adiabatic 
change. 

Relation  of  Adiabatic  and  Isothermal  Lines.— An  adia- 
batic line  drawn  on  the  (/,  v)  plane  is  steeper  than  an  isother- 
mal line  at  the  point  of  intersection.  This  is  easily  shown 
for  a  substance  that  expands  with  a  rise  of 
temperature.  Thus  let  ab  and  cd  (Fig.  5) 
represent  an  adiabatic  and  an  isothermal  line 
crossing  at  p.  The  substance  when  in  the 
condition  represented  by  the  point  p  has  a 
certain  volume,  pressure,  and  temperature. 
The  isothermal  change  represented  by  pd,  is 


FlG-  5-  at  constant  temperature.  On  the  other 

hand,  the  adiabatic  change  represented  by  pb,  is  accompanied 
by  a  loss  of  intrinsic  energy ;  but  the  intrinsic  energy  is  the 
sum  of  the  vibration  energy  and  the  disgregation  energy, 
and,  in  general,  a  loss  of  intrinsic  energy  means  a  diminution 
in  both  vibration  and  disgregation  energy.  Now  the  vibra- 
tion energy  is  represented  by  the  temperature,  and  the  tem- 
perature will  fall  when  the  vibration  energy  decreases.  Con- 
sequently the  temperature  at  b  is  less  than  the  temperature  at 
p,  and  therefore  is  less  than  the  temperature  at  d.  But  b 
and  d  are  at  the  same  pressure,  and  consequently  the  volume 
at  b  is  less  than  the  volume  at  d\  that  is,  the  adiabatic  line  is 
the  steeper. 

Graphical  Representations  of  Change  of  Intrinsic 
Energy. — Professor  Rankine  first  used  a  graphical  method  of 
representing  a  change  of  intrinsic  energy,  employing  adiabatic 
lines  only,  as  follows: 

Suppose  that  a  substance  is  originally  in  the  state  A  (Fig. 
6),  and  that  it  expands  adiabatically ;  then  the  external  work 
is  done  at  the  expense  of  the  intrinsic  energy ,  hence  if  the 
expansion  has  proceeded  to  Al  the  area  AA^a^a,  which  repre- 


FIAST  LAW   OF   THERMODYNAMICS.  21 

sents  the  external  work,  also  represents  the  change  of  intrinsic 
energy.  Suppose  that  the  expansion  were  to  continue  indefi- 
nitely :  then  the  adiabatic  will  approach  the 
axis  OV  indefinitely,  and  the  area  repre- 
senting the  work  will  be  included  between 
the  curve  Aa  produced  indefinitely,  the 
ordinate  Aa,  and  the  axis  OV\  this  area  will 
represent  all  the  work  that  can  be  obtained  *"  z>  a  5; 
by  the  expansion  of  the  substance ,  and  if  it 
be  admitted  that  during  the  expansion  all  the  intrinsic  energy  is 
transformed  into  work,  so  that  at  the  end  the  intrinsic  energy 
is  zero,  it  represents  also  the  intrinsic  energy.  In  cases  for 
which  the  equation  of  the  adiabatic  can  be  found  it  is  easy  to 
show  that 


\  =    I    pdv 

J  Vj 


is  a  finite  quantity  ;  and  in  any  case,  if  we  admit  an  absolute  zero 
of  temperature,  it  is  evident  that  the  intrinsic  energy  cannot 
be  infinite.  On  the  other  hand,  if  an  isothermal  curve  were 
treated  in  the  same  way  the  area  would  be  infinite,  since  heat 
would  be  continually  added  during  the  expansion. 

Now  suppose  the  body  to  pass  from  the  condition  repre- 
sented by  A  to  that  represented  by  B,  by  any  path  whatever — 
that  is,  by  any  succession  of  changes  whatever — for  example, 
that  represented  by  the  irregular  curve  AB.  The  intrinsic 
energy  in  the  state  B  is  represented  by  the  area  VbBfi.  The 
change  of  intrinsic  energy  is  represented  by  the  area  fiBbaAa, 
and  this  area  does  not  depend  on  the  form  of  the  curve  AB. 
This  graphical  process  is  only  another  way  of  saying  that  the 
intrinsic  energy  depends  on  the  state  of  the  substance  only, 
and  that  change  of  intrinsic  energy  depends  on  the  final  and 
initial  states  only. 

Another  way  of  representing  change  of  intrinsic  energy  by 


22 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


aid  of  isodynamic  lines  avoids  an  infinite  diagram.  Suppose 
the  change  of  state  to  be  represented  by  the 
curve  AB  (Fig.  7).  Draw  an  isodynamic  line 
AC  through  the  point  A,  and  an  adiabatic 
line  BC  through  B,  intersecting  at  C.  Then 
the  area  ABba  represents  the  external  work, 
and  the  area  bBCc  represents  the  change  of 
IG*  7<  intrinsic  energy  ;  for  if  the  body  be  allowed 

to  expand  adiabatically  till  the  intrinsic  energy  is  reduced  to 
its  original  amount  at  the  condition  represented  by  A  the 
external  work  bBCc  will  be  done  at  the  expense  of  the  intrinsic 
energy.  And  further,  since  the  intrinsic  energy  is  constant  for 
all  points  on  the  isodynamic  line  through  A,  and  in  like  man- 
ner is  constant  for  points  on  the  line  through  B,  there  will  be 
the  same  change  of  intrinsic  energy  in  passing  from  a  condition 
represented  by  any  point  of  the  line  through  A  to  any  point 
of  the  line  through  B\  consequently  if  through  any  point, 
as  D  of  the  upper  line,  an  adiabatic  DE  be  drawn  the  area 
dDEe  will  be  equal  to  bBCc,  and  will  equally  represent  the 
change  of  intrinsic  energy  from  the  point  A  to  the  point  B. 

Entropy. — If  a  body  have  its  condition  represented  by  the 
point  e  of  the  isothermal  aa^  (Fig.  8)  it  will  have  a  definite 
temperature,  which  will  be  the  same  so  long  as 
its  condition  is  represented  by  some  point  on 
aa^  as,  for  example,  e},  though  the  volume  and 
pressure  will  meanwhile  have  varied.  Should 
the  temperature  change,  the  condition  will 
represented 


a,  v 


be  represented  by  some  point,  as  f,  on 
another  isothermal  bb,.  There  will  evidently  be  the  same 
change  of  temperature  in  passing  from  e  to  f  as  from  et 
to/, ;  that  the  changes  of  volume  and  pressure,  external  work, 
and  intrinsic  energy  are  different  does  not  affect  the  statement 
concerning  the  temperature.  In  like  manner  it  is  indifferent 
how  or  at  what  part  of  the  diagram  the  transfer  from  bbl  to  ccl 
is  accomplished ;  the  same  change  of  temperature  must  occur. 
In  the  same  way  isoenergic  changes  will  be  represented  by 


FIRST  LAW  OF  THERMODYNAMICS.  2$ 

the  motion  of  a  point  along  a  curve  of  constant  energy ;  and 
there  will  be  a  definite  change  of  energy  in  passing  from  a 
curve  of  constant  energy  to  the  next  curve  of  a  system  of 
isoenergic  curves. 

Conversely,  if  we  have  any  system  of  curves  it  is  reason- 
able to  suppose  that  there  must  be  a  constant  change  of  some 
sort  in  passing  from  one  such  curve  to  the  next  of  the  same 
system.  A  series  of  adiabatic  curves  as  represented  by  Fig. 
9,  is  such  a  system  of  curves,  and  we  may  con- 
sider  that  there  is  the  same  change  in  passing 
from  e  to  /as  in  passing  from  et  to  /,,  e  being 
any  point  on  the  curve  aa,  and  f  being  any 
point  on  the  next  curve  bb^.  It  will  appear 
in  our  future  work  that  a  definite  form  may  FIG.  9. 
be  assigned  to  the  function  representing  the  change  that 
occurs  in  passing  from  one  adiabatic  line  of  a  given  sub- 
stance to  another  adiabatic  line  of  the  same  substance,  and 
that  a  numerical  calculation  may  be  made  representing  that 
change.  It  will  further  appear  that  the  form  of  the  function 
and  the  corresponding  numerical  calculation  will  depend  on 
the  nature  of  the  substance,  and  will  be  different  for  different 
substances.  For  exampje,  the  form  of  the  function  for  steam 
is  radically  different  from  the  form  for  air.  The  form  of  the 
function  is  consequently  a  property  of  the  substance,  just  as 
are  specific  volume  and  intrinsic  energy.  The  fact  that  the 
form  of  the  function  cannot  be  intelligently  explained  now, 
and  that  the  nature  is  different  from  other  properties  thus  far 
discussed,  is  no  reason  why  we  should  not  provide  for  the 
function,  give  it  a  name,  and  include  it  in  our  equations.  In 
the  proper  place  the  form  and  use  of  the  function  will  be  ex- 
plained. 

The  name  given  to  this  function  or  property  which  re- 
mains constant  during  an  adiabatic  change  is  entropy.  It  is 
commonly  represented  by  $.  5 

In  the  process  of  establishing  an  absolute  scale  of  temper- 
ature we  shall  show  how  a  system  of  isothermal  lines  can  be 


24  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

drawn  at  intervals  of  one  degree  of  temperature.  At  the 
same  time,  and  by  a  similar  method,  a  system  of  adiabatics 
will  be  drawn,  each  one  unit  of  entropy  from  the  next.  Both 
systems  of  lines  will  be  made  to  depend  on  the  foot-pound. 
It  may  be  suggested  further  that  thus  far  no  adequate  idea 
of  the  nature  of  temperature  has  been  obtained,  the  assertion 
that  temperature  is  in  some  way  connected  with  the  vibration 
energy  of  a  body  being  too  indefinite  for  this  purpose. 
Though  an  accepted  dictum  of  science,  it  remains  to  a.  certain 
extent  speculative.  Again,  for  the  engineer  it  is  more  im- 
portant to  be  able  to  calculate  changes  and  effects  than  to  be 
able  to  give  a  philosophical  account  of  their  real  nature. 


CHAPTER  III. 
SECOND   LAW   OF   THERMODYNAMICS. 

Heat-engines  are  engines  by  which  heat  is  transformed 
into  work.  All  actual  engines  used  as  motors  go  through  con- 
tinuous cycles  of  operations,  which  periodically  return  things 
to  the  original  conditions.  All  heat-engines  are  similar  in  that 
they  receive  heat  from  some  source,  transform  part  of  it  into 
work,  and  deliver  the  remainder  (minus  certain  losses)  to  a 
refrigerator. 

The  source  and  refrigerator  of  a  condensing  steam-engine 
are  the  furnace  and  the  condenser.  The  boiler  is  properly  con- 
sidered as  a  part  of  the  engine,  and  receives  heat  from  the 
source. 

Carnot's  Engine. — It  is  convenient  to  discuss  a  simple 
ideal  engine,  first  described  by  Carnot. 

Let  P  of  Fig.  10  represent  a  cylinder  with  non-conducting 
walls,  in  which  is  fitted  a  piston,  also  of  non-conducting  mate- 
rial, and  moving  without  friction  ;    on 
the  other   hand,  the    bottom    of  the 
cylinder  is  supposed  to  be  of  a  material 
that  is  a  perfect  conductor.      There  is 
a  non-conducting  stand   C  on  which    '     A      |  'u  c  u1 1     B 
the     cylinder    can    be    placed    while  FIG.  10. 

adiabatic  changes  take  place.  The  source  of  heat  A  at  a 
temperature  t  is  supposed  to  be  so  maintained  that  in 
operations  during  which  the  cylinder  is  placed  on  it,  and 
draws  heat  from  it,  the  temperature  is  unchanged.  The 
refrigerator  B  at  the  temperature  tv  in  like  manner  can  with- 

25 


26  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

draw  heat  from  the  cylinder,  when  it  is  placed  on  it,  at  a  con- 
stant temperature. 

Let  there  be  a  unit  of  weight  (for  example,  one  pound)  of 
a  certain  substance  in  the  cylinder  at  the  temperature  t  of  the 
source  of  heat.  Place  the  cylinder  on  the  source  of  heat  A 
(Fig.  10),  and  let  the  substance  expand  at  the  constant  tem- 
perature T,  receiving  heat  from  the  source  A. 

If  the  first  condition  of  the  substance  be 
represented  by  A  (Fig.  11),  then  the  second 
will  be  represented  by  B,  and  AB  will  be  an 
isothermal.  If  Ea  and  Eb  are  the  intrinsic 
energies  at  A  and  B.,  and  if  Wab,  represented 


FIG.  ii  by  the  area  aABb,  be  the  external  work,  the 

heat  received  from  A  will  be 

Q=A(JEb-Ea+  Wab). 

Now  place  the  cylinder  on  the  stand  £7  (Fig.  10),  and  let 
the  substance  expand  adiabatically  until  the  temperature  is 
reduced  to  Tlt  that  of  the  refrigerator,  the  change  being  rep- 
resented by  the  adiabatic  BC  (Fig.'  11).  If  Ee  is  the  intrinsic 
energy  at  C,  then,  since  no  heat  passes  into  or  out  of  the 
cylinder, 

E>  +  Wbc\ 


where  Wbc  is  the  external  work  represented  by  the  area  bBCc* 
Place  the  cylinder  on  the  refrigerator  B,  and  compress  the 
substance  till  it  passes  through  the  change  represented  by  CD, 
yielding  heat  to  the  refrigerator  so  that  the  temperature  re- 
mains constant.  If  Ed  is  the  intrinsic  energy  at  D,  then 

-  &  =  A(Ed  -Ec-  Wcd} 

is  the  heat  yielded  to  the  refrigerator,  and  Wcd,  represented  by 
the  area  cCDd,  is  the  external  work,  which  has  a  minus  sign> 
since  it  is  done  on  the  substances. 


SECOND    LAW  OF   THERMODYNAMICS.  2J 

The  point  D  is  determined  by  drawing  an  adiabatic  from 
A  to  intersect  an  isothermal  through  C.  The  process  is  com- 
pleted by  compressing  the  substance  while  the  cylinder  is  on 
the  stand  C  (Fig.  10)  till  the  temperature  rises  to  T,  the 
change  being  represented  by  the  adiabatic  DA.  Since  there 
is  no  transfer  of  heat, 

o  =  A(E.  -Ed-  Wda). 

Adding  together  the  several  equations,  member  to  mem- 
ber, 

Q-Ql=A(Wab+Wbc-  Wcd-  Wda); 

or,  if  Z^be  the  resulting  work  represented  by  the  area  A  BCD, 
then 


that  is,  the  difference  between  the  heat  received  and  the  heat 
delivered  to  the  refrigerator  is  the  heat  transformed  into  work. 

A  Reversible  Engine  is  one  that  may  run  either  in  the 
usual  manner,  transforming  heat  into  work,  or  reversed, 
describing  the  same  cycle  in  the  opposite  direction,  and  trans- 
forming work  into  heat. 

A  Reversible  Cycle  is  the  cycle  of  a  reversible  engine. 

Carnot's  engine  is  reversible,  the  reversed  cycle  being 
ADCBA  (Fig.  11),  during  which  work  is  done  by  the  engine 
on  the  working  substance.  The  engine  then  draws  from  the 
refrigerator  a  certain  quantity  of  heat,  it  transforms  a  certain 
quantity  of  work  into  heat,  and  delivers  the  sum  of  both  to 
the  source  of  heat. 

No  actual  heat-engine  is  reversible  in  the  sense  just  stated, 
for  when  the  order  of  operations  can  be  reversed,  changing 
the  engine  from  a  motor  into  a  pump  or  compressor,  the  re- 
versed cycle  differs  from  the  direct  cycle.  For  example,  the 
valve-gear  of  a  locomotive  may  be  reversed  while  the  train  is 
running,  and  then  the  cylinders  will  draw  gases  from  the 
smoke-box,  compress  them,  and  force  them  into  the  boiler. 


2  8  THERMOD  YNA  MICS   OF   THE   S  TEA  M-ENGINE. 

The  locomotive  as  ordinarily  built  is  seldom  reversed  in  this 
way,  as  the  hot  gases  from  the  smoke-box  injure  the  surfaces 
of  the  valves  and  cylinders.  Some  locomotives  have  been 
arranged  so  that  the  exhaust-nozzles  can  be  shut  off  and 
steam  and  water  supplied  to  the  exhaust-pipe,  thus  avoiding 
the  damage  from  hot  gases  when  the  engine  is  reversed 
in  this  way.  Such  an  engine  may  then  have  a  reversed  cycle, 
drawing  steam  into  the  cylinders,  compressing  and  forcing  it 
into  the  boiler;  but  in  any  case  the  reversed  cycle  differs 
from  the  direct  cycle,  and  the  engine  is  not  properly  a  revers- 
ible engine. 

A  Closed  Cycle  is  any  cycle  in  which  the  final  state  is  the 
same  as  the  initial  state.  Fig.  12  represents 
such  a  cycle  made  up  of  four  curves  of  any 
nature  whatever.  If  the  four  curves  are  of  two 

v_    species  only,  as  in   the   diagram   representing 

FIG.  12.  the  cycle  of  Carnot's  engine,  the  cycle  is  said 

to  be  simple.  In  general,  we  shall  have  for  a  cycle  like  that 
of  Fig.  12 


Wbc-  Wcd-  Wda\ 

A  closed  curve  of  any  form  may  be  consid- 
ered to  be  the  general  form  of  a  closed  cycle, 
as  that  in  Fig.  13.  For  such  a  cycle  we  have 

/  dQ  =  A  I  dW,  which  is  one  more  way  of 

stating  the  first  law  of  thermodynamics. 

It  may  make  this  last  clearer  to  con- 
sider the  cycle  of  Fig.  14,  composed  of  the 
isothermals  AB,  CD,  and  EG,  and  the 
adiabatics  BC,  DE,  and  GA.  The  cycle 

[o G^F~^E  v      may   be   divided   by   drawing   the  curve 

FIG.  14.  through   from  C  to  F.      It  is  indifferent 

whether  the  path  followed  be  ABCDEGA  or  ABCFCDEGA 
or,  again,  ABCFGA  +  CDEFC. 


SECOND    LAW  OF   THERMODYNAMICS.  2$ 

Again,  an  irregular  figure  may  be  imagined  to  be  cut  into 
elementary  areas  by  isothermals  and  adia- 
batic  lines,  as  in  Fig.  15.  The  summation 
of  the  areas  will  give  the  entire  area,  and 
the  summation  of  the  works  represented 
by  these  will  give  the  entire  work  repre- 
sented by  the  entire  area. 


The  Efficiency  of  an   engine  is  the  FIG.  15. 

ratio  of  the  heat  changed  into  work  to  the  entire  heat  applied  ; 
so  that  if  it  be  represented  by  rj, 


for  the  heat  Q  rejected  to  the  refrigerator  is  what  is  left  after 
A  W  thermal  units  have  been  changed  into  work. 

Carnot's  Principle.  —  It  was  first  pointed  out  by  Carnot 
that  the  efficiency  of  a  reversible  engine  does  not  depend  on 
the  nature  of  the  working  substance,  but  that  it  depends  on 
the  temperatures  of  the  source  of  heat  and  the  refrigerator. 

Let  us  see  what  would  be  the  consequence  if  this  princi- 
ple were  not  true.  Suppose  there  are  two  reversible  engines 
R  and  A,  each  taking  Q  thermal  units  per  second  from  the 
source  of  heat,  of  which  A  is  the  more  efficient,  so  that 


is  larger  than 


AW._Q-Q: 

~          ~~ 


AW,_Q-Q,'.  , 

Q  Q 


this  can  happen  only  because  Qaf  is  less  than  Qr',  for  Q  is  as- 
sumed to  be  the  same  for  each  engine.  Let  the  engine  R  be 
reversed  and  coupled  to  A,  which  can  run  it  and  still  have  left 
the  useful  work  Wa  —  Wr.  This  useful  work  cannot  come 
from  the  source  of  heat,  for  the  engine  R  when  reversed  gives 


30  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

to  the  source  Q  thermal  units  per  second,  and  A  takes  the 
same  amount  in  the  same  time.  It  must  be  assumed  to  come 
from  the  refrigerator,  which  received  Qa'  thermal  units  per 
second,  and  gives  up  Qr'  thermal  units  per  second,  so  that  it 
loses 


thermal  units  per  second.  This  equation  may  be  derived 
from  equations  (28)  and  (29)  by  subtraction. 

Now  it  cannot  be  proved  by  direct  experiment  that  such 
an  action  as  that  just  described  is  impossible.  Again,  the  first 
law  of  thermodynamics  is  scrupulously  regarded,  and  there  is 
no  contradiction  or  formal  absurdity  of  statement.  And  yet 
when  the  consequences  of  the  negation  of  Carnot's  principles 
are  clearly  set  forth  they  are  naturally  rejected  as  improbable, 
if  not  impossible.  The  justification  of  the  principle  is  found 
in  the  fact  that  theoretical  deductions  from  it  are  confirmed 
by  experiments. 

Second  Law  of  Thermodynamics. — The  formal  state- 
ment of  Carnot's  principle  is  known  as  the  second  law  of  ther- 
modynamics. Various  forms  are  given  by  different  investiga- 
tors, none  of  which  are  entirely  satisfactory,  for  the  conception 
is  not  simple,  as  is  that  of  the  first  law. 

The  following  are  some  of  the  statements  of  the  second 
law : 

(1)  All  reversible  engines  working  between  the  same  source 
of  heat  and  refrigerator  have  the  same  efficiency. 

(2)  The  efficiency  of  a  reversible  engine  is  independent  of 
the  working  substance. 

(3)  A  self-acting  machine  cannot  convey  heat  from  one  body 
to  another  at  a  higher  temperature. 

The  second  law  is  the  third  general  principle  of  thermo- 
dynamics ;  it  differs  from  each  of  the  others  and  is  independ- 
ent of  them.  Summing  up  briefly,  the  first  general  principle 
is  a  pure  assumption  that  thermodynamic  equations  may  con- 


SECOND    LAW   OF    THERMODYNAMICS.  31 

tain  only  two  independent  variables;  the  second  is  the  state- 
ment of  an  experimental  fact  ;  the  third  is  a  choice  of  one  of 
the  two  propositions  of  a  dilemma.  The  first  and  third  are 
justified  by  the  results  of  the  application  of  the  theory  of 
thermodynamics. 

Carnot's  Function.  —  Carnot's  principle  asserts  that  the 
efficiency  of  a  reversible  engine  is  independent  of  the  nature 
of  the  working  substance  ;  consequently  the  expression  for  the 
efficiency  will  not  include  such  properties  of  the  working  sub- 
stance as  specific  volume  and  specific  pressure.  But  the  prin- 
ciple asserts  also  that  the  efficiency  depends  on  the  tempera- 
tures of  the  source  of  heat  and  the  refrigerator,  which  indeed 
are  the  only  properties  of  the  source  and  refrigerator  that  can 
affect  the  working  of  the  engine. 

We  may  then  represent  the  efficiency  as  a  function  of  the 
temperatures  of  the  source  of  heat  and  the  refrigerator,  or,  what 
amounts  to  the  same  thing,  as  a  function  of  the  superior  tem- 
perature and  the  difference  of  the  temperatures,  and  may 
write 

_t,)t   ^      (3o) 


where  Q  is  the  heat  received,  Q  the  heat  rejected,  and  t  and 
/'  are  the  temperatures  of  the  source  of  heat  and  of  the  refrig- 
erator on  any  scale  whatsoever,  absolute  or  relative. 

If  the  temperature  of  the  refrigerator  approaches  near  that 
of  the  source  of  heat  Q  —  Q'  and  t  —  t'  become  AQ  and  J/, 
and  at  the  limit  dQ  and  dt,  so  that 


But  dt  is  itself  a  function  of  /,  so  that  at  the  limit  the  effi- 
ciency depends  on  /  only.  It  is  convenient  to  express  the 
equation  in  the  form 

=/(*)*.     ...     .     .    .     .     (32') 


32  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

An  algebraic  reduction  from  equation  (31)  to  (32)  may  be 
made  as  follows  :   divide,  and  multiply  by  dt,  so  that 


/(/)  is  called  Carnot's  function  and  is  represented  by 
so  that  the  efficiency  may  be  represented  by 


The  form  of  the  function  will  depend  on  the  scale  of  temper- 
ature selected  and  will  vary  from  one  scale  to  another  scale. 
The  logical  method  appears  to  be  to  choose  some  scale  of  tem- 
perature and  deduce  the  form  of  Carnot's  function  correspond- 
ing. The  easier  way  is  to  define  or  establish  an  arbitrary 
scale,  independent  of  any  special  thermometer  or  material, 
and  find  the  difference  between  that  scale  and  the  scale  of  a 
thermometer  such  as  the  air  thermometer  or  a  mercurial 
thermometer. 

Absolute  Scale  of  Temperature.—  The  simplest  form  that 

can  be  assigned  to   Carnot's   function   is  --  ,  where    T  is  the 

absolute  temperature  on  the  arbitrary  scale  corresponding  to 
that  form  of  Carnot's  function.  The  scale  of  temperature  so 
determined  is  the  absolute  scale  referred  to  on  page  5,  and 
depends  only  on  the  fundamental  units  the  foot  and  the 
pound,  or,  what  amounts  to  the  same  thing,  on  the  foot- 
pound. The  most  ready  way  of  showing  this  is  by  Thom- 
son's graphical  method. 

Thomson's  Graphical  Method.  —  The  method  just  given 
of  arriving  at  an  absolute  scale  independent  of  any  substance 
was  first  given  by  Lord  Kelvin,  who  further  explained  it  by 
the  following  graphical  construction  : 

In  Fig.  1  6  let  ak  and  bi  be   two   adiabatic   lines,    and  let 


SECOND   LAW  OF   THERMODYNAMICS.  33 

the  substance  have  its  condition  represented  by  the  point  a. 
Through  a  and  d  draw  iso- 
thermal lines;  then  the  dia- 
gram abed  represents  thecycle 
of  a  simple  reversible  engine. 
Draw  the  isothermal  line  fet 
so  that  the  area  dcefs\\3\\  be 
equal  to  abcd\  then  the  dia- 
gram dcef  represents  the  cycle 
of  a  reversible  engine,  doing 

the  same  amount  of  work  per  stroke  as  that  engine  whose  cycle 
is  represented  by  abed;  and  the  difference  between  the  heat 
drawn  from  the  source  and  delivered  to  the  refrigerater — i.  e., 
the  heat  transformed  into  work — is  the  same.  The  refrigerator 
of  the  first  engine  might  serve  for  the  source  of  heat  for  the 
second. 

Suppose  that  a  series  of  equal  areas  are  cut  off  by  isother- 
mal lines,  as/^/z,  hgik,  etc.,  and  suppose  there  are  a  series  of 
reversible  engines  corresponding :  then  there  will  be  a  series  of 
sources  of  heat  of  determinate  temperatures,  which  may  be 
chosen  to  establish  a  thermometric  scale.  In  order  to  have 
the  scale  correspond  with  those  of  ordinary  thermometers  one 
of  the  sources  of  heat  must  be  at  the  temperature  of  boiling 
water,  and  one  at  that  of  melting  ice ;  and  for  the  centi- 
grade scale  there  will  be  one  hundred,  and  for  the  Fahrenheit 
scale  one  hundred  and  eighty,  such  cycles,  with  the  appropriate 
sources  of  heat,  between  boiling-point  and  freezing-point.  To 
establish  the  absolute  zero  of  the  scale  the  series  must  be  im- 
agined to  be  continued  till  the  area  included  between  an  iso- 
thermal and  the  two  adiabatics,  continued  indefinitely,  shall 
not  be  greater  than  one  of  the  equal  areas. 

This  conception  of  the  absolute  zero  may  be  made  clearer 
by  taking  wide  intervals  of  temperature,  as  on  Fig.  1 7,  where  the 
cycle  abed  is  assumed  to  extend  between  the  isothermals  of  o°* 
and  1 00°  C.  ;  that  is,  from  freezing-point  to  boiling-point.  The 
next  cycle,  cdef,  extends  to  —  100°  C.,and  the  third  cycle,  efghr 


34 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


•extends  to  —200°  C. 


The  remaining  area,  which  is  of  infinite 
length  and  extremely  attenuated, 
is  bounded  by  the  isothermal  gh 
and  the  two  adiabatics  ha  and^y?. 
The  diagram  of  course  cannot  be 
completed,  and  consequently  the 
area  cannot  be  measured ;  but 
when  the  equations  to  the  isother- 
mal and  the  adiabatics  are  known 
it  can  be  computed.  So  com- 
puted, the  area  is  found  to  be 


73-7 
100 


of    one   of    the  three  equal 


FIG.  17. 


areas  abed,  cdfe,  and  efhg.     The 
absolute     zero     is      consequently 
v  273°.  7    C.    below    freezing-point. 
Further  discussion  of  the  absolute 


scale  will  be  deferred  till  a  comparison  is  made  with  the  air- 
thermometer. 

Scale  of  Entropy.  —  A  similar  treatment  may  be  given 
to  the  scale  of  entropy.  Thus  in  Fig.  18  let  the  iso- 
thermals  ab  and  cd  be  ex- 
tended indefinitely,  and  let 
a  series  of  adiabatics  be 
drawn,  cutting  off  equal  areas 
abed,  blmc,  and  Inom,  etc.  ; 
we  shall  then  have  a  series  of 
intervals  of  entropy  depend- 
ing on  the  foot-pound.  To 
make  the  scale  of  entropy 
definite  we  will  assume  that 
the  isothermals  an  and  do 


FIG.  18. 

are  one  degree  apart,  and  that  the  initial  cycle  abcd\s  so  drawn 
that  it  represents  the  change  of  one  thermal  unit  into  work : 
for  the  English  system  the  area  abed  represents  778  foot- 
pounds. 


SECOND    LAW  OF   THERMODYNAMICS.  35 

Now  the  area  beneath  an  isothermal  line  extending  indefi- 
nitely is  infinite,  for  heat  is  continually  added  to  the  working 
substance  to  keep  up  the  temperature,  and  there  is  no  limit  to 
the  amount  of  work  that  can  be  done  by  expansion.  In  this 
regard  the  isothermal  is  radically  different  from  the  adiabatic, 
for  an  infinite  adiabatic  expansion  is  supposed  to  change  all 
the  intrinsic  energy  of  the  working  substance  into  external 
work  ;  and  as  the  intrinsic  energy  is  finite,  so  also  must  be  the 
area  representing  external  work.  We  may  conclude  that  the 
area  bounded  by  the  adiabatic  ad,  and  the  two  isothermals 
an  and  do,  is  infinite,  and  that  there  is  no  limit  to  the  number 
of  equal  areas  that  can  be  cut  off  by  equally  spaced  adiabatics. 

It  will  be  noted  that  on  the  diagram  the  adiabatic  no  is 
higher  than  the  adiabatic  ad,  so  that  the  entropy  increases 
from  a  towards  n.  The  area  of  the  strip  between  the  adia- 
batic be  and  the  isothermals  bat  and  cd,  both  extended  indefi- 
nitely towards  the  left,  is  infinite;  consequently  there  is  no 
absolute  zero  of  entropy,  and  we  shall  therefore  be  able  to 
calculate  differences  of  entropy  only.  The  area  of  the  typical 
cycle  chosen  for  measuring  intervals  of  entropy  is  large  (equal 
to  778  foot-pounds)  ;  consequently  the  numbers  expressing 
changes  of  entropy  will  be  found  to  be  small. 

Efficiency  of  Reversible  Engines,  —  The  general  differ- 
ential equation  for  the  efficiency  of  a  reversible  engine  is 


-        =f(f)dt  = 


or,  making  Carnot's  function  equal  to  ^~, 


^ 
Q         T 

Integrating  between  limits, 

Q  f, 


3  6  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

QL-7! 

•'*     Q  ~'  T' 

Q-Q'_T-r 

Q  ~T       '      ••"••     (33) 

The  absolute  scale  of  temperature  consequently  depends 
only  on  the  efficiency  of  a  reversible  engine,  and  since  the  ef- 
ficiency of  such  an  engine  is  independent  of  the  properties  of 
any  substance,  so  also  is  the  absolute  scale.  The  efficiency  is 
expressed  in  thermal  units,  which  are  equivalent  to  the  proper 
number  of  mechanical  units  (foot-pounds) ;  consequently  the 
absolute  scale  of  temperature  may  be  made  to  depend  directly 
on  the  foot-pound — that  is,  on  the  fundamental  units  the  foot 
and  the  pound.  This  discussion  is  only  another  way  of  view- 
ing the  ideas  discussed  by  Thomson's  graphical  method. 
Graphical  Representation  of  Efficiency. — -Let  Fig.  19 
represent  the  cycle  of  a  reversible  heat- 
engine.  For  convenience  it  is  supposed 
there  are  four  degrees  of  temperature 
from  the  isothermal  AB  to  the  isother- 
mal DC,  and  that  there  are  three  inter- 
vals or  units  of  entropy  between  the 
adiabatics  AD  and  BC.  First  it  will  be 
-shown  that  all  the  small  areas  into  which 


the  cycle  is  divided  by  drawing  the  inter- 
vening adiabatics  and  isothermals  are  equal.  Thus  we  have 
to  begin  with  a  =  b  and  a  =  c  by  construction.  But  engines 
working  on  the  cycles  a  and  b  have  the  same  efficiency  and 
reject  the  same  amounts  of  heat.  These  heats  rejected  are 
equal  to  the  heats  supplied  to  engines  working  on  the  cycles 
c  and  d,  which  consequently  take  in  the  same  amounts  of  heat. 
But  these  engines  work  between  the  same  limits  of  tempefa- 
ture  and  have  the  same  efficiency,  and  consequently  change 
the  same  amount  of  heat  into  work.  Therefore  the  areas  c 
and  d  are  equal.  In  like  manner  all  the  small  areas  are  equal, 


SECOND   LAW  OF   THERMODYNAMICS.  37 

and  each  represents  one  thermal  unit,  or   778   foot-pounds  of 
work. 

It  is  evident   that  the  heat  changed   into  work  is  repre- 
sented by 


(34) 


and,  further,  that  the  same  expression  would  be  obtained  for  a 
similar  diagram,  whatever  number  of  degrees  there  might  be 
between  the  isothermals,  or  intervals  of  entropy  between  the 
adiabatics,  and  that  it  is  not  invalidated  by  using  fractions  of 
degrees  and  fractions  of  units  of  entropy.  It  is  consequently 
the  general  expression  for  the  heat  changed  into  work  by  an 
engine  having  a  reversible  cycle. 

It  is  clear  that  the  work  done  on  such  a  cycle  increases  as 
the  lower  temperature  T'  decreases,  and  that  it  is  a  maximum 
when  T'  becomes  zero,  for  which  condition  all  of  the  heat 
applied  is  changed  into  work.  Therefore  the  heat  applied  is 
represented  by 

Q  =  T(<t>'  -  0),  ......     (35) 

and  the  efficiency  of  the  engine  working  on  the  cycle  repre- 
sented by  Fig.  19  is 

AW  _  Q-Q       (T-  r')(0'-0)       T-  T' 
Q  Q  7X0'  -0)  T 

as  found  by  equation  (33).  .The  deduction  of  this  equation 
by  integration  is  more  simple  and  direct,  but  the  graphical 
method  is  interesting  and  may  give  the  student  additional 
light  on  this  subject. 

Temperature  —  Entropy  Diagram.  —  Thermal  diagrams 
are  commonly  drawn  with  pressure  and  volume  for  the  coordi- 
nates, but  for  some  purposes  it  is  convenient  to  use  temperature 
and  entropy.  Thus  Carnot's  cycle,  when  temperature  and 


38  THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

entropy  are  used  for  coordinates,  becomes  a  rectangle,  as 
shown  by  Fig.  20.  As  in  Fig.  19,  four  de-/ 
grees  of  temperature  and  three  intervals  of 
entropy  have  been  chosen,  and  the  diagram  is 
subdivided  into  twelve  equal  areas,  which  in 
-  Fig.  20  are  evidently  equal,  as  they  are  all 
rectangles. 


FIG.  20. 


Expression    for    Entropy. 

(35)  f°r  the  heat  supplied  P 
along  the  isothermal  line  AB 
(Fig.  19),  it  appears  that  the 
amount  of  heat  supplied  de- 
pends on  the  temperature  T 
and  on  the  difference  of  en- 
tropy 0'  —  0.  The  amount 
of  heat  will  decrease  as  the 
interval  of  entropy  decreases, 
and  will  approach  dQ  when 
0'  —  0  approaches  d<t>,  as 
shown  by  Fig.  21,  so  that 


Resuming   the   expression 


FIG.  21. 


dQ  =  Td<t>, 


or 


(36) 


or,  integrating  between  limits, 


dQ 
T' 


(37) 


Equation  (37)  may  be  used  for  calculating  the  change 
of  entropy  during  any  reversible  operation,  provided  that  the 
heat  added  may  be  expressed  as  a  function  of  the  temperature* 


SECOND    LAW  OF   THERMODYNAMICS.  39 

For  example,  we  may  calculate  the  change  of  entropy 
from  A  to  B  (Fig.  19)  as  follows: 

The  temperature  during  the  isothermal  expansion  from  A 
to  B  is  constant,  therefore  the  heat  added  is  due  entirely  to 
the  latent  heat  of  expansion,  and  we  have  from  equation  (5) 

dQ  =  Idv. 

For  a  perfect  gas  the  latent  heat  of  expansion  is  given 
by  equation  (66),  page  63,  so  that 

dQ  =  (cp  -  cv}^Ldv. 
But  R  =  -^ ;  consequently 

,.  _  dQ  _  dv 


.'.       0'   -    0   =    (Cp  —  Cv)    log,   -. 


Suppose  that  vb  is  8  cubic  feet,  and  va  is  4  cubic  feet,  then 

g 

<p  —  </>=  (0.2375  —  0.1690)  log,  —  , 

4 

when  the  values  of  cp  and  c,  for  air  are  used,  giving  finally 

0  —  0'  =  0.0685  X  0.6931  =  O.O475 

for  the  increase  of  entropy  corresponding  to  the  isothermal 
expansion  from  A  to  B. 

Application  to  a  Reversible  Cycle.  —  A  very  important 
result  is  obtained  by  the  application  of  equation  (37)  to  the 
calculation  of  entropy  during  a  reversible  cycle.  In  the  first 
place,  it  is  clear  that  the  entropy  of  a  substance  having  its 
condition  represented  by  the  point  a  (Fig.  22),  depends  on  the 


4O  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

adiabatic  line  drawn  through  it ;  in  other  words,  the  entropy 

depends  only  on  the  condition  of 
the  substance.  In  this  regard 
entropy  is  like  intrinsic  energy 
and  differs  from  external  work. 
Suppose  now  that  the  substance 
v  is  made  to  pass  through  a  cycle 


FIG.  22.  of  operations,  represented  by  the 

point  a  tracing  the  diagram  on  Fig.  22  :  it  is  clear  that  the 
entropy  will  be  the  same  at  the  end  of  the  cycle  as  at  the 
beginning,  for  the  tracing-point  will  then  be  on  the  original 
adiabatic  line.  As  the  tracing-point  moves  toward  the  right 
from  adiabatic  to  adiabatic  the  entropy  increases,  and  as 
it  moves  to  the  left  the  entropy  decreases,  the  algebraic  sum 
of  changes  of  entropy  being  zero  for  the  entire  cycle.  This 
conclusion  holds  whether  the  cycle  is  reversible  or  non- 
reversible. 

If  the  cycle  is  reversible,  then  equation  (37)  may  be  used  for 
calculating  the  several  changes  of  entropy,  and  for  calculating 
the  change  for  the  entire  cycle,  giving  for  the  cycle 


(38) 


This  is  a  very  important  conclusion  from  the  second  law  of 
thermodynamics,  and  is  considered  to  represent  that  law.  The 
second  law  is  frequently  applied  by  using  this  equation  in  con- 
nection with  a  general  equation  or  a  characteristic  equation, 
in  a  manner  to  be  explained  later. 

Though  the  discussion  just  given  is  simple  and  complete, 
there  is  some  advantage  in  showing  that  equation  (38)  holds 
for  certain  simple  and  complex  reversible  cycles. 

Thus  for  Carnot's  cycle,  represented  by  Fig.  19,  the 
increase  of  entropy  during  isothermal  expansion  is 


0'-  ^  =  f'A  =  _L  fdQ  = 
J     T         TJ 


SECOND   LAW  OF   THERMODYNAMICS  4 1 

because  the   temperature   is  constant.      In    like  manner  the 
decrease  during  isothermal  expansion  is 


so  that  the  change  of  entropy  for  the  cycle  is 


G_ 
T 


QL 

T 


But  from  the  efficiency  of  the  cycle  we  have 


.  a 

'  '  Q 


T 
T 


Q       Q 
T       F  = 


A  complex  cycle  like  that  represented  by  Fig.  23  may  be 

broken  up  into  two  simple  cycles  ABFG 

and  CDFE,  for  each  of  which  individually 

the  same  result  will  be  obtained  —  that  is, 

the  increase  of  entropy  from  A   to  B  is 

equal  to  the  decrease  from  F  to  G,   and 

the  increase  from  C  to  D  is  equal  to  the 

decrease  from  E  to  F,  so  that  the  sum-  FlG-  23-  . 

mation  of  changes  for  the  entire  cycle  gives  zero. 

Fig.  24  represents  the  simplified  ideal  diagram  of  a  hot-air 

engine,   in  which   by  the  aid  of  a  regenerator  the  adiabatic 

lines  of  Carnot's  cycle  are  re- 
placed by  vertical  lines  without 
affecting  the  reversibility  or  the 
efficiency  of  the  cycle.  We  may 
replace  the  actual  diagram  by  a 
series  of  simple  cycles  made  up  of 
isothermals  and  adiabatics,  so 
drawn  that  the  perimeter  of  the 
y  complex  cycle  includes  the  same 
area  and  corresponds  approxi- 
The  summation  of 


FIG.  24. 
mately  with  that  of  the  actual  diagram. 


42  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

the  change  of  entropy  for  the  complex  cycle  is  clearly  zero,  as 
before.  But  by  drawing  the  adiabatic  lines  near  enough  to- 
gether we  may  make  the  perimeter  approach  that  of  the  actual 
diagram  as  nearly  as  we  please,  and  we  may  therefore  con- 
clude that  the  integration  for  the  changes  of  entropy  for  that 
cycle  is  also  zero. 

Non-reversible  Cycles. — If  a  process  or  a  cycle  is  non- 
reversible,  then  the  change  of  entropy  cannot  be  calculated  by 
equation  (37),  and  equation  (38)  will  not  hold.  The  entropy 
will,  indeed,  be  the  same  at  the  end  as  at  the  beginning  of  the 

cycle,  but  the  integration  of  -^  for  the  cycle  will  not  give 
zero.  On  the  contrary,  it  can  be  shown  that  the  integration 
of  -=-  for  the  entire  cycle  will  give  a  negative  quantity. 

Thus  let  the  non-reversible  engine  A  take  the  same  amount 
of  heat  per  stroke  as  the  reversible  engine  R  which  works  on 
Carnot's  cycle,  but  let  it  have  a  less  efficiency,  so  that 

Q-  Q/      Q-Q' 

Q  ~Q~~>        ....     (39) 

where  Qt'  represents  the  heat  rejected  by  the  engine  A. 
Then 

Q  ~  Q,'  <  Q  -  Q'  =  (T-  n(0'-  0).    •     .     (40) 

Suppose  now  that  T  approaches  zero  and  that  0'  approaches 
0,  then  at  the  limit  we  shall  have 

dQ,  <dQ  =  Tdfr 
or 

dQ. 
T 

Integrating  for  the  entire  cycle,  we  shall  have 


SECOND   LAW  OF   THERMODYNAMICS.  43 

where  N  represents  a  negative  quantity.  The  absolute  value 
of  N  will,  of  course,  depend  on  the  efficiency  of  the  non-re- 
versible engine.  If  the  efficiency  is  small  compared  with  that 
of  a  reversible  engine,  then  the  value  of  N  will  be  large.  If 
the  efficiency  approaches  that  of  a  reversible  engine,  then  N 
approaches  zero.  It  is  scarcely  necessary  to  point  out  that  N 
cannot  be  positive,  for  that  would  infer  that  the  non-reversi- 
ble engine  had  a  greater  efficiency  than  a  reversible  engine 
working  between  the  same  temperatures. 

Some  non-reversible  operations,  like  the  flow  of  gas 
through  an  orifice,  result  in  the  development  of  kinetic  en- 
ergy of  motion.  In  such  case  the  equation  representing  the 
distribution  of  energy  contains  a  fourth  term  K  to  represent 
the  kinetic  energy,  and  equation  (22)  becomes 

dQ  =  A(dS+dI+dW+dK\   .     .     .     (42) 

As  before  5  represents  vibration  work,  /  represents  disgre- 
gation  work,  and  W  represents  external  work.  If  the  vibration 
and  disgregation  work  cannot  be  separated,  then  we  may  write 

(43) 


CHAPTER    IV. 
FUDNAMENTAL   EQUATIONS. 

Application  of  the  First  Law. — The  application  of  the 
first  law  of  thermodynamics  consists  in  uniting  an  equation 
resulting  from  that  law  to  some  general  or  some  characteristic 
equation.  For  example,  equations  (5)  and  (23)  give 

dQ  =  A(dE  +  dW)  =  cvdt  +  Idv, 
or,  replacing  dWby  pdv, 

A(dE  +  pdv)  =  cvdt  +  Idv. 

l--p}dv.     ...     (44) 

Now  E  depends  on  the  state  of  the  body  only,  and  not  on 
the  method  of  changing  from  one  condition  to  another;  that 
is,  dE  is  an  exact  differential,  and  consequently 


dtdv       dvdt' 
which  may  be  written 


'f)l  JX^) 

^dt'-»  V  =  •<     ^dv't 


dv      )  t       (       dt 

'        C  \  f         v 

44 


FUNDAMENTAL   EQUATIONS.  45 

in  which  the  partial  differential  coefficients  are  those  of  the 
equation 


Comparing  with  equation  (44),  it  appears  that 
ldE\       cv  ldE\       II         \ 

ttsjjfcrg         UH^-^' 

and  that  consequently 


dv\A)t~~  dt 
iridl\ 


,     , 


Equation  (45)  represents  the  relation  which  must  exist  be- 
,ween  the  latent  heat  of  expansion  and  the  specific  heat  at 
constant  volume  in  consequence  of  the  first  law  of  thermody- 
namics. In  order  that  the  relation  may  be  developed  for 
some  particular  substance,  such  as  air,  the  partial  differential 

coefficient  f-^j   must  be  deduced  from  the  characteristic  equa- 
\dt'  * 

tion.     The  use  of  this  and  of  similar  succeeding  equations  can 
be  determined  only  by  the  application  of  the  theory  of  ther 
modynamics  to  various  substances. 

In  a  similar  manner  the  first  law  may  be  applied  to  equa- 
tion (6),  as  follows: 


dQ  =  A(dE  +  pdv)  =  cpdt  +  mdp. 
Substituting  the  value  of  dv  from  the  equation 
tdv\    ,t       idv\ 


*=(!),*+ ©* 


46  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

«*  ; 


But 


dtdp~  dpdt' 


i_ldc,\  _  (fa  \dt  i_(dm\ 

A\dp)t      \dt)p     P\    dp    Jt     A\dt)p 

But 

dp  dt  ~  dt  dp  ' 

•  •  •  (46> 


which  is  the  relation  between  the  thermal  capacity  m  and  the 
specific  heat  at  constant  pressure  developed  by  the  application 
of  the  first  law  to  equation  (6). 

Again,  the  same  law  may  be  applied  to  the  equation  (7). 

dQ  =  A(dE  -\-pdv)  =  ndp-\-  odv  ; 
•'•  dE  =  ^dp  +  (^-p}dv  .....     ,     (47) 
Since 


dpdv~  dvdp1 

-      V-^  --  l(do\       i- 
'   ~A\dv}p-~  A\dpir 


FUNDAMENTAL   EQUATIONS.  47 

Application  of  the    Second  Law — The    second  law  of 

dQ 

thermodynamics  is  expressed  by  making  -y.  an  exact  differen- 
tial as  indicated  by  equations  (36)  and  (38).  Applying  this 
to  equation  (5)  in  the  same  way  as  was  done  with  the  first  law, 


But 


or 


, 

* 


(dQ  CdQ 

•J  T        Jr. 


dtdv"  dv  dt  -dt  dv  dv  dt 

\-      d(1^ 

L  *(T). 


_^/£i\-    ±iL\  . 


dt)r  i 


the  relation  between  /  and  cv  developed  by  the  application  of 
the  second  law  to  equation  (5). 

Applying  to  equation  (6),  we  have 


— 
dp\T)r  dt 


—  m 


T  HER  MOD  YNAMICS   OF   THE   STEAM-ENGINE. 


Again,  applying  to  equation  (7), 


dQ        n   ,         o   , 
JSL  =   —dp  J  __  dv, 
T        T        h  T 


dt  idt 


First  and  Second  Laws  Combined. — The  result  of  ap- 
plying both  the  first  and  second  laws  of  thermodynamics 
simultaneously  to  the  fundamental  equations  is  deduced  by 
uniting  the  equations  obtained  by  applying  each  separately. 

For  the  equation  (5),  in  terms  of  cv  and  /,  the  comparison 
of  equations  (45)  and  (49)  gives 

®)=zi §  (52> 

For  equation  (6)  the  comparison  of  equations  (46)  and  (50) 
gives 

idv\  i   m 

(53) 

For  equation  (7)  the  comparison  of  equations  (48)  and  (51) 
gives 

dt 


or,  substituting  the  values  of  n  and  o  from  equations  (17)  and 
(i  8), 

-  • 

(55) 


FUNDAMENTAL   EQUATIONS.  49 

Alternative  Method.  —  Some  writers  on  thermodynamics 
reserve  the  discussion  of  temperature  until  they  are  ready 
to  define  or  assume  an  absolute  scale  independent  of  any 
substance,  and  depending  only  on  the  fundamental  units  of 
length  and  weight.  Of  the  three  general  equations  (5),  (6), 
and  (7)  they  use  at  first  only  the  latter: 

dQ  =  ndp  +  odv. 

Now  from  the  equation  (23),  representing  the  first  law  of 
thermodynamics, 


it  is  evident  that  dQ  is  not  an  exact  differential,  since  the 
equation  cannot  be  integrated  directly.  The  fact  that  in  cer- 
tain cases/  may  be  expressed  as  a  function  of  z/,  and  the  inte- 
gral for  external  work  can  be  deduced,  does  not  affect  this 
general  statement.  Suppose  that  there  is  some  integrating 

factor,  which  may  be  represented  by  —  ,  so  that 

o 


may  be  integrated  directly:   we  may  then  consider  that  we 
have  a  series  of  thermal  lines  represented  by  making 

—  =  const.,       — -  =  const.,       ~^r/  =  const.,  etc. 
o  o  o 

These  lines  with  a  series  of  adiabatic  lines  represented  by 
0  =  const.,         0'  =  const.,         0"  =  const.,  etc., 

allow  us  to  draw  a  simple  cycle  of  operations  represented  by 


50  THERMODYNAMICS   OF  THE  STEAM-ENGINE. 

Fig.  25,  in  which  AB  and  CD  are   represented  by  the   equa- 
tions 

p 

-7,=  6",    and     -~.  =  £7', 


while  AD  and  /761  are  adiabatics.      The  ef- 

15 Ll    ficiency  of  a  reversible  engine  receiving  the 

heat  Q  during  the   operation  AB,  and  re- 
jecting the  heat  Q  during  the  operation  £77, will  be 


But  -~-  is  an  exact  differential,  and  depends  on  the  state 

of  the  substance  only,  and  consequently  is  the  same  at  the  end 
as  at  the  beginning  of  the  cycle,  so  that   for  the  entire  cycle 


s 


Now  during  the  operations  represented  by  the  adiabatics 
AD  and  BC  no  heat   is  transmitted,  and  during  the  opera- 

tions represented  by  the  lines  AB  and  CD  -^  is  constant;  con- 

sequently the  integration  of  the  above  equation  for  the  cycle 
gives 

Q     Q 


Q-Q  _S-S> 

Q  s 

that    is,    the    efficiency    of    an    engine   working  on    such    a 
cycle  depends  on  5  and  S',  and  on  nothing  else. 


FUNDAMENTAL  EQUATIONS.  5  I 

Let  us  now  define  absolute  temperature  by  making 

T=S, 

so  that  we  have 

Q  -  Q'       T  -  T' 


~Q  T      ' 

and  we  will  have  a  scale  of  temperature  depending  only  on 
the  efficiency  of  a  reversible  engine,  and  consequently  inde- 
pendent of  the  properties  of  any  substance. 

The  discussion  just  given  comes  properly  after  the  state- 
ment of  the  first  and  second  laws  of  thermodynamics,  and  is 
followed  by  the  application  of  those  laws. 

Zeuner's  Kquations.  —  In  his  Mechanische  Wdrmetheorie 
Zeuner  employs  the  alternative  method  so  far  as  to  deducing 
equation  (41).  Then,  instead  of  assuming  that  5  is  the  abso- 
lute temperature,  or  giving  such  a  definition  of  temperature, 
he  assumes  that  the  similarity  of  the  thermodynamic  equa- 
tions to  certain  gravitation  equations  indicates  an  essential 
similarity,  and  thereby  avoids  the  second  law  of  thermody- 
namics. Without  discussing  his  method,  there  appears  no 
reason  why  it  might  not  be  applied  to  deduce  equations  of 
the  same  form  as  those  given  on  pages  44  to  48.  He,  how- 
ever, gives  equations  of  a  different  form  which  may  readily  be 
deduced  from  our  own,  and  which  it  may  be  convenient  to 
write  down  here.  Comparing  equation  (47)  with 

•»-(*)*+(£),* 

it  is  evident  that 


7  =  (?}' 
A        \dpl, 


dE 


52  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

These  Zeuner  writes: 


Solving  equation  (54)  for  o  and  for  n, 


o  = 


Substituting  the  value  for  o  in  equation  (7),  we  have 


But 


Again,  substituting  the  value  for 


, 


FUNDAMENTAL  EQUATIONS.  53 

Zeuner  gives  for  his  fundamental  equations 

Ydv)\ 


\d 


p 


which  may  readily  be  deduced   from  equation    (23)  and  the 
equations  above. 

These  equations  are  set  down  here  because  they  are  com- 
monly used  by  German  writers  in  discussing  thermodynamics. 


CHAPTER  V. 
PERFECT  GASES. 

THE  characteristic  equation  for  a  perfect  gas  is  derived 
from  a  combination  of  the  laws  of  Boyle  and  Gay-Lussacr 
which  may  be  stated  as  follows : 

Boyle's  Law. — When  a  given  weight  of  a  perfect  gas 
is  compressed  (or  expanded)  at  a  constant  temperature  the 
product  of  the  pressure  and  the  volume  is  a  constant.  This 
law  is  nearly  true  at  ordinary  temperatures  and  pressures  for 
such  gases  as  oxygen,  hydrogen,  and  nitrogen.  Gases  which 
are  readily  liquefied  by  pressure  at  ordinary  temperatures,  such 
as  ammonia  and  carbonic  acid,  show  a  notable  deviation  from 
this  law.  The  law  may  be  expressed  by  the  equation 

pv=Av>, (56) 

in  which  pl  and  vl  are  the  initial  pressure  and  volume ;  /  is  any 
pressure  and  v  is  the  corresponding  volume. 

Gay-Lussac's  Law. — It  was  found  by  Guy-Lussac  that 
any  volume  of  gas  at  freezing-point  increases  about  0.003665 
of  its  volume  for  each  degree  rise  of  temperature.  Gases 
which  are  easily  liquified  deviate  from  this  law  as  well  as 
from  Boyle's  law.  In  the  deduction  of  this  law  temperatures 
were  measured  on  or  referred  to  the  air-thermometer,  and  the 
law  therefore  asserts  that  the  expansibility  or  the  coefficient  of 
dilatation  of  perfect  gases  is  the  same  as  that  of  air.  It  will 
be  shown  in  this  chapter  that  the  scale  of  the  air-thermometer 
differs  but  little  from  that  of  the  absolute  thermodynamic 

54 


PERFECT  GASES.  55 

scale  ;  for  practical  purposes  the  difference  may  be  neglected. 
Gay-Lussac's  law  may  be  expressed  by  the  equation 

v  =  v.(i  +  «$)  .     -     -     '.     •     •     (57) 

in  which  vg  is  the  original  volume  at  freezing-point,  ot  is  the 
coefficient  of  dilatation  or  the  increase  of  volume  for  one 
degree  rise  of  temperature,  and  v  is  the  volume  corresponding 
to  the  temperature  /  measured  from  freezing-point. 

Coefficient  of  Dilatation. — Regnault*  gives  for  the  dila- 
tation from  freezing-  to  boiling-point  at  Paris  the  results : 

Hydrogen 0.003667 

Atmospheric  air 0.003665 

Nitrogen 0.003668 

Carbonic  acid 0.003688 

In  works  on  thermodynamics  it  has  been  commonly  as- 
sumed that  the  coefficient  of  dilatation  for  air  may  be  used  for 
all  gases,  and  at  all  temperatures  and  pressures,  and  that,  con- 
sequently, on  the  centigrade  scale  a  is  0.003665,  or  very 

nearly  — '.      Professor  Holman  f  suggests  that  as  the  pressure 

approaches    zero    the    coefficient    of    dilatation    of   all    gases 

approaches 

I 

a  = , 

273.7 

which  agrees  with  thermodynamic  investigations  relating  to  the 
absolute  zero  of  temperature.  On  the  Fahrenheit  scale 

i 

a  = . 

492.7 

Characteristic  Equation. — From  equation  (57)  we  may 
calculate  any  special  volume,  such  as  z/,,  getting 


*  Me'moires  de  f  Institut  de  France,  tome  xxi. 

\  Lecture  Notes  on  Heat,  Mass.  Inst.  Technology. 


56  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Assuming  that  pl  in  equation  (56)  is  the  normal  pressure  of 
the  atmosphere  /0,  and  substituting  the  value  just  found  for  vlt 
we  have  for  the  combination  of  the  laws  of  Boyle  and  Gay- 
Lussac 

•      -      (5*0 


If  now  we  assume  that  a  perfect  gas  contracts  -  part 

273-7  1 

of  its  volume  at  freezing-point  for  each  degree  decrease  of 
temperature,  then  the  absolute  zero  of  temperature  on  the 
scale  of  the  air-thermometer  is  273°. 7  C.  below  freezing-point ; 
and  centigrade  temperatures  can  be  transformed  into  absolute 
temperatures  by  adding  273°.  7.  In  like  manner  the  zero  of  the 
air-thermometer  on  the  Fahrenheit  scale  is  492°.  7  below  freez- 
ing-point, which  on  that  scale  is  at  32°;  and  absolute  tem- 
peratures will  be  obtained  by  adding  460°.  7  to  the  Fahrenheit 
temperatures. 

The  usual  form  of  the  characteristic  equation  for  perfect 
gases  may  be  derived  from  equation  (58)  by  substituting  T9, 

the  absolute  temperature  of  freezing-point,  for  — ,  giving 


(59) 

•*  o 

where  R  is  a  constant  representing  the  quantity 


For  solution  of  examples  it  is  more  convenient  to  write 
equation  (59)  in  the  form 

PV       p.v, 

-?  =  -jr.     .     .     .     .     .     .     (60) 


PERFECT   GASES.  57 

Absolute  Temperatures. — For  convenient  reference  it  is 
desirable  to  write  down  the  equations 

T  =  t  +  273°. 7  centigrade  scale, 
T  =  t  -f-  460°. 7  Fahrenheit  scale, 

in  which  /  is  the  ordinary  temperature  by  the  thermometer 
and  T  is  the  absolute  temperature. 

Relation  of  French  and  English  Units — Both  French 
and  English  standard  units  of  length  and  weight  are  arbitrary 
standards  represented  by  the  length  of  bars  or  the  weight  of 
certain  pieces  of  metal.  The  French  metre  is  the  length 
from  end  to  end  of  a  bar  of  platinum  at  freezing-point;  the 
English  yard  is  the  length  from  one  line  to  another  on  a 
bronze  bar  at  62°  F.  ;  owing  to  the  different  methods  of  de- 
fining the  standards,  comparisons  are  very  difficult.  The  ratio 
of  the  lengths  of  the  standards  used  in  this  book  is  that  given 
by  Professor  Rogers,*  namely, 

one  metre  =  39.3702  inches. 

The  last  figure,  2,  is  probably  uncertain  to  the  extent  of 
one  unit.  For  engineering  work  the  metre  may  be  assumed 
to  be  equal  to  39.37  inches. 

The  ratio  of  the  standards  of  weight  f  is 

one  kilogram  =  2.20462125  pounds. 

Acceleration  due  to  Gravity.— The  force  with  which  a 
body  is  attracted  towards  the  earth  is  proportional  to  the 
acceleration  due  to  gravity,  and  varies  with  the  latitude  and 
with  the  altitude  above  sea-level,  as  given  by  the  equation  \ 

g  —  980.6056  —  2.5028  cos  2\  —  0.000003/2,     .  (61) 


*  Proc.  Am.  Acad.  of  Arts  and  Sci.t  1882-83;  also  additional  observations, 
f  Miller,  Phil.  Transactions,  cxlvi,  1856. 
\  Everett's  Units  and  Phys.  Const. 


58  THERMOD  YNAM1CS   OF   THE   STEAM-ENGINE. 

in  which  g  is  the  acceleration  in  centimetres  per  second,  A.  is 
the  latitude,  and  h  is  the  altitude  above  the  sea  in  centimetres. 

Standard  Latitude. — It  is  customary  to  reduce  all  physi- 
cal observations  which  are  affected  by  the  attraction  of  gravity 
to  the  latitude  of  45°  and  to  sea-level.  This  reduction  affects 
the  fifth  significant  figure,  and  consequently  is  properly 
recognized  in  recording  physical  constants  which  may  be 
used  by  engineers,  but  it  is  seldom,  if  ever,  necessary  for  an 
engineer  to  reduce  such  physical  constants  to  the  place  where 
he  may  be  located. 

Specific  Pressure.— The  normal  pressure  of  the  atmos- 
phere is  assumed  to  be  equivalent  to  that  of  a  column  of 
mercury  760  mm.  high  at  freezing-point.  Now  Regnault  * 
gives  for  the  weight  of  a  litre,  or  one  cubic  decimetre,  of 
mercury  1 3. 5959  kilograms ;  consequently  the  specific  pressure 
of  the  atmosphere  under  normal  conditions  is 

p0  =  10333  kilograms  per  square  metre. 

Using  the  conversion  units  given  above  for  reducing  this 
specific  pressure  to  the  English  system  of  units  gives 

/0  =  21^6.32  pounds  per  square  foot, 
which  corresponds  to. 

14.6967  pounds  per  square  inch, 
or  to 

29.921  inches  of  mercury. 

It  is  customary  and  sufficient  to  use  for  the  pressure  of  the 
atmosphere  14.7  pounds  to  the  square  inch. 

*  MJmoires  de  flnstitut  de  France,    vol.  xxi. 


PERFECT  GASES.  59 

Densities  of  Gases.  —  The  weights  in  kilograms  of  one 
cubic  metre  of  several  gases,  as  determined  by  Regnault,  are 
given  in  the  following  table: 

Atmospheric  air  ...............  1  .293  1  87 

Nitrogen  .....................  1.256167 

Oxygen  ......................  1  .429802 

Hydrogen  ....................  0.089578 

Carbonic  acid  .................  i  .977414 

Now  the  acceleration  due  to  gravity  at  Paris,  as  calculated 
by  equation  (61),  is  980.9218  centimetres,  while  the  acceler- 
ation at  45°  latitude  and  at  sea-level  is  980.6056  centimetres; 
consequently  the  pressure  due  to  760  mm.  of  mercury  at  45° 
latitude  is  equivalent  to  that  of  only 


at  Paris,  and  the  weights  of  one  cubic  metre  of  the  several  gases 
at  the  normal  pressure  of  the  atmosphere  will  be  smaller  in  a 
like  proportion.  To  get  the  specific  volumes  we  may  multiply 
the  weights  by  the  ratio 

759-755 
760 

and  then  take  the  reciprocal  of  the  results,  giving  results  set 
down  in  the  following  paragraph. 

Specific  Volumes.  —  The  following  table  gives  the  specific 
volumes  of  several  gases  in  cubic  metres  per  kilogram  : 

VOLUMES   IN    CUBIC     METRES    OF   ONE    KILOGRAM 
AT   45°  OF    LATITUDE. 

Atmospheric  air  .............  °-7735327 

Nitrogen  ...................  0.7963291 

Oxygen  ....................  0.699623  1 

Hydrogen  ..................  1  1.16705 

Carbonic  acid  ...............  o.  5058741 


60  THERMODYNAMICS   OF   7  'HE   STEAM-ENGINE. 

The  corresponding  quantities  for  English  units  are  given 
in  the  next  table  : 

VOLUMES  IN  CUBIC  FEET  OF  ONE  POUND  AT  45°  OF  LATITUDE. 

Atmospheric  air  ...............      12.3909 

Nitrogen  .....................      12.7561 

Oxygen  ......................       11.2070 

Hydrogen  ....................  178.881 

Carbonic  acid  .............  ....  8.  10324 

Value  of  R.  —  The  constant  R  which  appears  in  the  usual 
form  of  the  characteristic  equation  for  a  gas  represents  the 
expression 


The  values  for  R  corresponding  to  the  French  and   the 
English  system  of  units  may  be  calculated  as  follows: 


French  units,  R  =  !°333  X  °'77^  =  29.20.        (62) 

273-7 

T?         V    l.  r>  2II6.3    X     I2.3QI  ,,.     N 

English  units,  R  =  --  —       _2z__  =53.22.   .    (63) 

492.7 

Value  of  R  for  other  gases  may  be  calculated  in  a  like 
manner. 

Solution  of  Problems.—  Many  problems  involving  the 
properties  of  air  or  other  gases  may  be  solved  by  the  charac- 
teristic equation 

pv  =  RTy 

or  by  the  equivalent  equation 


T.' 


which  for  general  use  is  the  more  convenient. 


PERFECT  GASES.  6 1 

In  the  first  of  these  two  equations  the  specific  pressure  and 
volume  to  be  used  for  English  measures  are  pounds  per  square 
foot,  and  the  volume  in  cubic  feet  of  one  pound. 

For  example,  let  it  be  required  to  find  the  volume  of  3 
pounds  of  air  at  60  pounds  gauge-pressure  and  at  100°  F. 
Assuming  a  barometric  pressure  of  14.7  pounds  per  square 
inch, 

53.22(460.7  +  100) 

v  =       ,     ^  —  =  2.774  cubic  feet 

(14.7+60)144 

is  the  volume  of   I  pound  of  air  under  the  given  conditions, 
and  3  pounds  will  have  a  volume  of 

3  X  2.774  =  8.322  cubic  feet. 

The  second  equation  has  the  advantage  that  any  units  may 
be  used,  and  that  it  need  not  be  restricted  to  one  unit  of 
weight. 

For  example,  let  the  volume  of  a  given  weight  of  gas,  at 
100°  C.  and  at  atmospheric  pressure,  be  2  cubic  yards;  re- 
quired the  volume  at  200°  C.  and  at  10  atmospheres.  Here 

\£>v         i  X  2 


473-7    "   373-7  ' 

2   =  °'2535 


Application  of  the  Laws  of  Thermodynamics.  —  Equa 

tion  (55),  page  48, 


which  was  deduced  by  applying  both  laws  of  thermodynamics 
to  equation  (7),  may  be  most  conveniently  used  in  this  place. 


62  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Differentiating  the  characteristic  equation 

pv  =  RT, 
we  obtain 


ldv\    _R 

\dtip  ~  7' 


tf 
v* 


which  substituted  in  equation  (55)  gives 

cp-cv=AR.        .     .     .     ...     (64) 

Specific  Heat  at  Constant  Pressure — The  specific  heat 
for  true  gases  is  very  nearly  constant,  and  may  be  considered 
to  be  so  for  thermodynamic  equations.  Regnault  gives  for 
the  mean  values  for  specific  heat  at  constant  pressure  the  fol- 
lowing results : 

Atmospheric  air 0.2375 

Nitrogen 0.2438 

Oxygen 0.2 175 

Hydrogen 3-4-O9 

Specific  Heat  at  Constant  Volume.— It  is  evident  from 
inspection  of  equation  (64)  that  the  specific  heat  at  constant 
volume  is  a  constant,  and  that  equation  also  gives  one  of  the 
best  ways  of  calculating  this  quantity.  Most  commonly  the 
ratio  of  the  two  specific  heats  is  determined,  as  follows : 


(65) 


K  = 


l          10333  x  0.77353 

426.9  X  273.7  X  0.2375 
K  =  1.4046  =  1.405,  nearly. 


PERFECT  GASES.  63 

Thermal  Capacities. — Substituting  the  values  of  the  par- 
tial differential  coefficients  as  deduced  from  equation  (59),  in 
equations  (11),  (15),  17),  and  (18),  we  have  for  the  values  of 
the  thermal  capacities  for  gases 


_,.);     .       .        .       (66) 


v  T 

=--g(cp-c,)=-  -(*>-*,);    .     .     (67) 


1*  =  ?*! (68) 


P  .        T 


General  Equations. — To  deduce  the  general  equations 
for  gases  from  equations  (5),  (6),  and  (7)  it  is  only  necessary 
to  replace  the  letters  /,  m,  n,  and  o  by  their  values  just  ob- 
tained, giving 


-do;     ....     (70) 


,-cpy-dp\     .     .     .     .     (71) 


dQ  =  c-pdp  +  cp-dv (72) 


64  THERMO D  YNAMICS   OF   THE   STEAM-ENGINE. 

Isothermal  Line — The  equation  to  the  isothermal  line 
for  a  gas  is  obtained  by  making  T  a  constant  in  the  character- 
istic equation,  so  that 


or 

pv  =  A^,.  (73) 

f    *f  X     II  \/\J/ 

This  equation  will  be  recognized  as  the  expression  of 
Boyle's  law.  It  is,  of  course,  the  equation  to  an  equilateral 
hyperbola. 

To  obtain  the  external  work  during  an  isothermal  expan- 
sion we  may  substitute  for  /  in  the  expression 

W  = 

from  the  equation  to  the  isothermal  line  just  stated,  using 
for  limits  the  final  and  initial  volumes,  v9  and  vl : 


^A^'f=/^Jog,g 


W'.^p^  j     --=/,*;,  log, -'.      .     .     .     (74) 

If  the  problem  in  any  case  calls  for  the  external  work  of 
one  unit  of  weight  of  a  gas,  then  vl  and  v^  must  be  the  initial 
and  final  specific  volumes;  but  in  many  cases  the  initial  and 
final  volumes  are  given  without  any  reference  to  a  weight, 
and  it  is  then  sufficient  to  find  the  external  work  for  the  given 
expansion  from  the  initial  to  the  final  volume  without  con- 
sidering whether  or  not  they  are  specific  volumes. 

The  pressures  must  always  be  specific  pressures ;  in  the 
English  system  the  pressures  must  be  expressed  in  pounds  on 
the  square  foot  before  using  them  in  the  equation  for  external 
work  or,  for  that  matter,  in  any  thermodynamic  equation. 

For  example,  the  specific  volume  of  air  at  freezing-point  and 
at  14.7  pounds  pressure  per  square  inch  is  about  12.4  cubic 
feet;  at  the  same  temperature  and  at  29.4  pounds  per  square 
inch  the  specific  volume  is  6.2  cubic  feet.  The  external  work 


PERFECT   GASES.  6$ 

during  an  isothermal  expansion  of  one  pound  of  air  from  6.2 
to  12.4  cubic  feet  is 


—  29.4  X  H4  X  6.2  log,  — —  =  18190  foot-pounds. 

For  example,  the  external  work  of  isothermal  expansion 
from  3  cubic  feet  and  60  pounds  pressure  by  the  gauge  to  a 
volume  of  7  cubic  feet  is 

W=  (60+  14.7)144  X  3  log,  -  =  27340  foot-pounds. 

In  both  problems  the  pressure  per  square  inch  is  multi- 
plied by  144  to  reduce  it  to  the  square  foot.  In  the  first 
problem  the  pressures  are  absolute,  that  is,  they  are  measured 
from  zero  pressure;  in  the  second  problem  the  pressure  by 
the  gauge  is  60  pounds  above  the  pressure  of  the  atmosphere, 
which  is  here  assumed  to  be  14.7  pounds  per  square  inch,  and 
is  added  to  give  the  absolute  pressure.  In  careful  ex- 
perimental work  the  pressure  of  the  atmosphere  is  measured 
by  a  barometer  and  is  added  to  the  gauge-pressure. 

Isoenergic  Line. — The  isothermal  line  for  a  perfect  gas 
is  also  the  isoenergic  line,  a  fact  that  may  be  proved  as 
follows:  The  heat  applied  during  an  isothermal  expansion 
may  be  calculated  by  making  T  a  constant  in  equation  (70) 
and  then  integrating ;  thus  : 


Q  =  (ft-  c.)Tt  =  (ft  -  c.)  Tt  log,  *  , 

%J  J'j  1 

or,  substituting  for  cp  —  cv  from  equation  (64), 


i  l°g*  —  =  AP\V\  log*  —  •       •     •     (75) 
v.  v. 


OF    THK 


66  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

A  comparison  of  equation  (75)  with  equation  (74)  shows 
that  the  heat  applied  during  an  isothermal  expansion  is  equiv- 
.alent  to  the  external  work,  or  we  may  say  that  all  the  heat 
applied  is  changed  into  external  work,  so  that  the  intrinsic 
energy  is  not  changed. 

An  interesting  corollary  of  the  discussion  just  given  is  that 
;an  infinite  isothermal  expansion  gives  an   infinite  amount   of 
work.       Thus     the    area    contained    between 
the  axis  OV  (Fig.  26),    the  ordinate  ab,  and 
the     isothermal     line    aa    extended    without 

limit  is 
a 

Tr,  .         oo 

W=.p<Vi    log,—  =  00. 


FIG.  26. 

This  may  also  be  seen  from  the  consideration  that  if  heat 
be  continually  applied,  and  all  changed  into  work,  there  will 
be  a  limitless  supply  of  work. 

Adiabatic  Lines.  —  During  an  adiabatic  change  —  for  exam- 
ple, the  expansion  of  a  gas  in  a  non-conducting  cylinder  —  heat 
is  not  communicated  to,  nor  abstracted  from,  the  gas;  conse- 
quently dQ  in  equations  (70),  (71),  and  (72)  becomes  zero. 

From  equation  (72) 


cpdv  _       dp  f 

~'~    ~ 


The  ratio  —  of  the  specific  heats  may  be  represented  by  /r, 

£91 


ind  the  above  equation  may  be  written 


-H; (76) 

v*p  =  vfpt  =  const (77) 


PERFECT  GASES.  6/ 

This  is  the  adiabatic  equation  for  a  perfect  gas  which  is 
most  frequently  used.  If  adiabatic  equations  involving  other 
variables,  such  as  vl  and  7^  ,  are  desired,  they  may  be  derived 
from  equation  (76)  by  aid  of  the  characteristic  equation,  which 
for  this  purpose  may  be  written 

pv  _p,v, 
T  "  "   T>  ' 
so  that 


and 


.-.     7V<-'  =  7X-*.       .....     (79) 

Or  equations  (78)  and  (79)  may  be  deduced  directly  from 
equation  (70)  as  equations  (76)  and  (77)  were  from  equa- 
tion (72). 

In  like  manner  we  may  deduce  from  equation  (71) 


(80) 


or  we  may  derive  it  from  equation  (76). 
To  find  the  external  work  the  equation 


W=        pdv 
maybe  used  after  substituting  for/  from  equation  (77): 

W=   r  pdv  =  tvy,  /***  =  _ 

'  ' 


68  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

In  Fig.  27  the  area  between  the  axis  OV> 
the  ordinate  da,  and  the  adiabatic  line  act  ex- 
tended without  limit  becomes 


FIG.  27. 

and  not  infinity,  as  is  the  case  with  the  isothermal  line. 

Here,  as  with  the  calculation  of  external  work  during  iso- 
thermal expansion,  specific  volumes  should  be  used  when  the 
problem  involves  a  unit  of  weight ;  but  work  may  be  calcul- 
ated for  any  given  initial  and  final  volumes  without  consider- 
ing whether  they  are  specific  volumes  or  not.  The  pressures 
are  always  pounds  on  the  square  foot  for  the  English 
system. 

For  example,  the  external  work  of  adiabatic  expansion 
from  3  cubic  feet  and  60  pounds  pressure  by  the  gauge  to  the 
volume  of  7  cubic  feet  is 


W=      -  ,  _  =  ^^  foot.pounds> 


which  is  considerably  less  than  the  work  for  the  correspond- 
ing isothermal  expansion. 

Intrinsic  Energy.  —  Since  external  work  during  an  adia- 
batic expansion  is  done  at  the  expense  of  the  intrinsic 
energy,  the  work  obtainable  by  an  infinite  expansion  can- 
not be  greater  than  the  intrinsic  energy.  If  it  be  admit- 
ted that  such  an  expansion  changes  all  of  the  intrinsic  energy 
into  external  work  we  shall  have 


K  —    I 


(82) 


which  gives  a  ready  way  of  calculating  intrinsic  energy.  In 
practice  we  always  deal  with  differences  of  intrinsic  energy, 
so  that  even  if  there  be  a  residual  intrinsic  energy  after  an 


PERFECT  GASES.  69 

infinite  adiabatic  expansion  the  error  of  our  method  will  be 
eliminated  from  an  equation  having  the  form 

E  -E  =-^     •-*&-,  (83) 

^«  -    K  -  l  K  _  j  ' 

Exponential  Equation.  —  The  expansions  and  compres- 
sions of  air  and  other  gases  in  practice  are  seldom  exactly 
isothermal  or  adiabatic  ;  more  commonly  an  actual  operation 
is  intermediate  between  the  two.  It  is  convenient  and 
usually  sufficient  to  represent  such  expansions  by  an  exponen- 
tial equation, 

/^=A*V>     ......    (84) 

in  which  n  has  a  value  between  unity  and  1.405.  The  form 
of  integration  for  external  work  is  the  same  as  for  that  of 
adiabatic  expansion,  and  the  amount  of  external  work  is  inter- 
mediate between  that  for  adiabatic  and  that  for  isothermal 
expansion. 

Change  of  temperature  during  such  an  expansion  may  be 
calculated  by  the  equations 

7V-'=  TX*-',    .....     (85) 

n  (Q£\ 

*     ..... 


which    may  be    deduced   from    equation  (82)  by  aid  of  the 
characteristic  equation 


as  equation  (79)  is  deduced  from  equation  (76). 

If  it  is  desired  to  find  the  exponent  of  an  equation  repre- 
senting a  curve  passing  through  two  points,  as  al  and  #,  (Fig. 
28),  we  may  proceed  by  taking  logarithms  of 
both  sides  of  the  equation 


giving 

n  log  z\  -|-  log  p\  =  »  log  z/s  +  log  A»  FlG*  28> 


70  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

so  that 


For  example,  the  exponent  of  an  equation  to  a  curve  pass- 
ing through  the  points 

A  =  74-  7,     ^  =  3>     and    /2  =  30,    ^a  =  7 
is 

log  74.7  -  log  30 


log  7  —  log  3 
Entropy. — For  any  reversible  process 


=  1.104. 


consequently  from  equations  (70),  (71),  and  (72)  we  have 


'  dt  dv 

=  ^-  +    (cp  -  <:,)— , 


and,  integrating  between  limits, 


-  tf.)     log,  ~,    .      (88) 


PERFECT   GASES.  7 1 

r,  p, 

c>  log,  7;    +  (o  -  '.)  log,  l~»     -     (89) 


0.  -  0,  =  ^  log,  .     +  *>  log,      ,      .     .       .     (90) 


which  give  ready  means  of  calculating  changes  of  entropy. 

For  example,  the  change  of  entropy  in  passing  from  the 
pressure  of  74.7  pounds  absolute  per  square  inch  and  the 
volume  of  3  cubic  feet  to  the  pressure  of  30  pounds  absolute 
and  the  volume  of  7  cubic  feet  is 

0.2375  ,         30 


Since  the  pressures  form  the  numerator  and  denominator 
of  a  fraction,  there  is  no  necessity  to  reduce  them  to  the 
square  foot.  In  this  problem  the  pressures  and  volumes  are 
taken  at  random;  they  correspond  to  a  temperature  of  146* 
F.  at  the  initial  condition. 

Comparison  of  the  Air-thermometer  with  the  Absolute 
Scale. — In  connection  with  the  isodynamic  line  it  was  shown 
that  the  intrinsic  energy  is  a  function  of  the  temperature  only.. 
This  conclusion  is  deduced  from  the  characteristic  equation 
on  the  assumption  that  the  scale  of  the  air-thermometer  coin- 
cides with  the  thermodynamic  scale,  and  it  affords  a  delicate 
method  of  testing  the  truth  of  the  characteristic  equation,  and 
of  comparing  the  two  scales. 

The  most  complete  experiments  for  this  purpose  were 
made  by  Joule  and  Sir  William  Thomson,  who  forced  air 
slowly  through  a  porous  plug  in  a  tube  in  such  a  manner  that 
no  heat  was  transmitted  to  or  from  the  air  during  the  process. 
Also  the  velocity  both  before  and  beyond  the  plug  was  so 
small  that  the  work  due  to  the  change  of  velocity  could  be 
disregarded.  All  the  work  that  would  be  developed  in  free 


72  THERMOD  YNAMICS    OF   7 HE   STEAM-ENGINE. 

expansion  from  the  higher  to  the  lower  pressure  was  used  in 
overcoming  the  resistance  of  friction  in  the  plug,  and  so  con- 
verted into  heat,  and  as  none  of  this  heat  escaped  it  was  re- 
tained by  the  air  itself,  the  plug  remaining  at  a  constant  tem- 
perature. It  therefore  appears  that  the  intrinsic  energy  re- 
mained the  same,  and  that  a  change  of  temperature  indicated 
a  deviation  from  the  assumptions  of  the  theory  of  perfect 
gases. 

In  the  discussion  of  results  given  by  Joule  and  Thomson  * 
in  1854  they  give  for  the  absolute  temperature  of  freezing- 
point  2  73°.  7  C.  As  the  result  of  later  f  experiments  they 
state  that  the  cooling  for  a  difference  of  pressure  of  100  inches 
of  mercury  is  represented  on  the  centigrade  scale  by 


The  following  table  shows  the   agreement   between   this 
statement  and  the  results  of  experiment : 


FLOW    OF    AIR    THROUGH   POROUS  PLUG, 


Cooling  Effect  : 

By  Experiment. 

By  Calculation. 

0° 

0.92 

0.92 

7-1 

0.88 

0.87 

39.5 

0.75 

0.70 

92.8 

0.51 

0.51 

From  the  work  of  these  experiments  Rowland  $  deduced 
the  following  comparison  of  the  air-thermometer  at  constant 
volume  with  the  absolute  thermodynamic  scale  of  temperature  : 

*  Philosophical  Transactions ,  vol.  144,  p.  349. 

\  Ibid.,  vol.  152,  p.  579. 

\  Proceedings  of  the  American  Academy^  vol.  xv  (N.  S.  viii),  p.  75,  1879. 


PERFECT   GASES. 


73 


REDUCTION    OF    THE   AIR-THERMOMETER   TO    THE 
ABSOLUTE   SCALE. 

(Centigrade. ) 


Temperature  above  Freezing. 

Correction  to  Air- 
thermometer. 

Air-thermometer. 

Absolute  Scale. 

0° 

0 

0 

IO 

9.9972 

—  0.0028 

2O 

19.9952 

—  0.0048 

30 

29.9939 

—  0.0061 

40 

39-9933 

—  0.0067 

50 

49.9932 

—  0.0068 

60 

59-9937 

—  0.0063 

70 

69.9946 

-  0.0054 

80 

79.9956 

—  0.0044 

90 

89.9978 

—   O.OO22 

100 

IOO.OOO 

O. 

2OO 

200.037 

+  0.037 

300 

300.092 

+  0.092 

400 

400.157 

+  0.157 

500 

500.228 

-J-  0.228 

Velocity  of  Sound.  — Sound  is  transmitted  through  the 
air  in  spherical  waves,  but  at  a  distance  from  the  source  of 
sound  the  waves  are  sensibly  plane  waves,  c  •  B 

and  the  progress  of  the  wave  is  the  same 
as  that  of  a  plane  wave  in  a  straight  tube 
of  uniform  section.      Let  Fig.  29  repre- 
sent a  tube  one  square  metre  in    section    in  which  a  wave 
moves  with  a  linear  velocity  «0  metres  per  second ;   that  is,  a 
point  at  a  given   phase  of  the  wave — for  example,  C  at  the 
greatest  condensation — moves  at  that  velocity. 

Since  the  wave  moves  with  the  velocity  u0,  the  volume  of 
air  disturbed  in  a  unit  of  time  is  u0  cubic  metres.  If  the 
specific  volume  in  the  undisturbed  state  is  z/0,  then  the  weight 
of  air  disturbed  in  a  second  is 


m  being  the  mass  of  air  which  has  the  weight  w. 


74  THERMODYNAMICS    OF   THE   STEAM-ENGINE. 

Imagine  two  planes  A  and  B  at  a  small  distance  apart,  which 
also  move  with  the  velocity  «0,  so  that  they  remain  at  the  same 
phase  of  the  wave.  Let  the  absolute  velocities  of  the  air  at 
these  planes  be  u^  and  &3 ;  then  the  velocities  of  the  air 
through  the  planes — that  is,  the  velocities  relatively  to  the 
planes — is,  for  A,  UQ—U^  and  for  B,  ?/0  —  //„.  With  vt  and 
v^  for  the  specific  volumes  at  these  planes  the  weights  that 
pass  through  the  planes  A  and  B  per  second  are 

,        u0  —  uz 
and 


Since  the  phase  of  that  portion  of  the  wave  between  A  and 
B  is  constant,  the  weight  of  the  air  between  them  is  also  con- 
stant, and  as  much  air  enters  per  second  as  leaves  during  that 
time.  Again  :  as,  on  the  whole,  the  air  is  not  transmitted,  but 
only  compressed  and  rarefied,  the  whole  air  disturbed  per 
second  must  pass  through  the  space  between  the  planes. 
Therefore 


=        = 


ut  -  u,  =  mgv9  -  v,}. 

Now  as  the  mass  m  enters  the  space  between  the  planes 
with  the  absolute  velocity  ult  and  an  equal  mass  leaves  with 
the  velocity  #2,  consequently  there  is  a  change  of  momentum 


and  since  this  cannot  come  from  the  mutual  action  of  the  par- 
ticles, it  must  come  from  the  difference  of  pressures  at  A  and 
B\  thus: 

A  -A  —  M«i  —  O 


PERFECT   GASES.  7$ 

As  the  planes  A  and  B  approach  each  other  /,  and/a,  z/t 
and  v^  approach  in  value,  and  at  the  limit 

dp  =  —  m*gdvt 


the  last  reduction  being  obtained  by  substituting  for  the  value 
of  m  from  the  preceding  work.      Solving  for  u,  , 

dp 
u.=-^~ 

The  vibrations  are  so  rapid  that  the  changes  of  state  may 
be  assumed  to  be  adiabatic  ;   consequently  equation  (72)  gives 


dv 


The  planes  A  and  B  may  be  taken  at  any  phase  of  the 
wave;  for  example  at  the  phase  where  the  pressure  and  vol- 
ume are  normal  in  which  case 


-         . 
dv  v,' 

Substituting  in  the  equation  for  «8,  we  have 


The  equation  is  commonly  given  in  terms  of  the  density, 
X,  as  follows; 


(90 


76  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  velocity  of  sound  from  direct  experiment  was  found 
by  Moll  and  Van  Beek  to  be  332.26  metres  per  second;  by 
Regnault  to  be  330.70  metres  per  second.  Kayser  found 
from  Kundt's  dust  figures  the  wave  length  corresponding  to  a 
certain  tone,  and  therefrom  deduced  the  velocity  of  sound,  and 
gives  for  the  velocity  332.50  metres  per  second.  The  true 
value  must  be  nearly  332  metres  per  second.  Solving  equa- 
tion (91)  for  /c,  and  inserting  the  known  values  of  pji\  and  g 
for  Paris, 


332 


'  gv.p.       9.8092  X  0.77328  X  10333  ' 

K    =    1.4063. 

This  result  as  calculated  compares  very  well  with  that 
already  calculated  by  aid  of  equation  (65),  but  it  depends 
entirely  on  the  value  assigned  to  the  velocity  of  sound 
whether  the  comparison  is  satisfactory  or  not.  Now  that  the 
determination  of  the  mechanical  equivalent  of  heat  by  Row- 
land has  reduced  the  probable  error  of  that  physical  constant 
to  a  small  amount  the  calculation  by  equation  (65;  is  to  be 
preferred  especially  as  it  agrees  very  well  with  the  results  ot 
direct  experiments  by  Rontgen. 

Rontgerrs  Experiments, — Direct  experiments  to  deter- 
mine K  may  be  made  as  follows  •  Suppose  that  a  vessel  is 
filled  with  air  at  a  pressure  /,  ,  while  the  pressure  ot  the 
atmosphere  is  pa.  Let  a  communication  be  opened  with  the 
atmosphere  sufficient  to  suddenly  equalize  the  pressure ;  then 
let  it  be  closed,  and  let  the  pressure  /„  be  observed  after  the 
air  has  again  attained  the  temperature  of  the  atmosphere 
If  the  first  operation  is  sufficiently  rapid  it  may  be  assumed 
to  be  adiabatic,  and  we  may  use  equation  (77),  from  which 


(92) 


. 

log  v.  —  log  v, 


PERFECT  GASES.  77 

The  second  operation  is  at  constant  volume  ;  consequently 
the  specific  volume  is  the  same  at  the  final  state  as  after  the 
adiabatic  expansion  of  the  first  operation.  But  the  initial  and 
final  temperatures  are  the  same ;  consequently 


.-.      log  va—  log  z/,  =  log/,  —  log/,, 
which  substituted  in  equation  (92)  gives 

JC_logA  -log A  ,    . 

-log A -log A" 

The  same  experiment  may  be  made  by  rarefying  the  air  in 
the  vessel,  in  which  case  the  sign  of  the  second  term  changes. 

Rontgen  *  employed  this  method,  using  a  vessel  contain- 
ing 70  litres,  and  measuring  the  pressure  with  a  gauge  made 
on  the  same  principle  as  the  aneroid  barometer.  Instead  of 
assuming  the  pressure /„  at  the  instant  of  closing  the  stop-cock 
to  be  that  of  the  atmosphere,  he  measured  it  with  the  same 
instrument.  A  mean  of  ten  experiments  on  air  gave 

K  =  1.4053- 

The  value  which  will  be  used  in  this  book  for  the  ratio  of 
the  specific  heats  of  air  is 

K    =CJ=    1.405. 

C9 

EXAMPLES. 

1 .  Find  the  weight  of  4  cubic  metres  of  hydrogen  at  30°  C 
and  under  the  pressure  of  800  mm.  of  mercury.     Ans.  0.3398 

kg- 

2.  Find  the  volume  of  3  pounds  of  nitrogen  at  a  pressure 
of  45  pounds  to  the  square  inch  by  the  gauge  and  at  80°  F. 
Ans.    10.34  cu.  ft. 

*  Poggendorff's  Annalen,  vol.  cxlviii,  p.  580. 


78  THERMOD  YNAMICS    OF   THE   STEAM-ENGINE. 

3.  Find  the  temperature  at  which  one  kilogram  of  air  will 
occupy  one  cubic  metre  when  at  a  pressure  of  20,000  kilograms 
per  square  metre.      Ans.   4iic.2C. 

4.  Find  the  pressure  at  which  2   pounds  of  carbonic  acid 
at  freezing-point  of  water  will  occupy  3  cubic  feet.     Ans.    79.4 
pounds  per  sq.  in. 

5.  A  gas-receiver  having  the  volume  of  3  cubic  feet  con- 
tains half  a   pound  of  oxygen   at    70°  F.      What  is  the  press- 
ure?     Ans.    29.6  pounds  per  sq.  in. 

6.  A  spherical  balloon  20  feet  in  diameter  is  to  be  inflated 
with  hydrogen  at  6oc  F.  when  the   barometer  stands  at  30.2 
inches,  so  that  gas  may  not  be  lost  on  account  of  expansion 
when  it  has  risen  till  the  barometer  stands  at  19.6  inches  and 
the   temperature  falls  to  40°  F.      How  many  pounds  and  how 
many  cubic  feet  are  to  be  run   in?      Ans.    15.1    pounds,  2828 
cu.  ft. 

7.  A  gas-receiver  holds   14  ounces  of  nitrogen  at  20°  C. 
and  under  a  pressure  of  29.6  inches  of  mercury.      How  many 
will  it  hold  at  32°  F.  and  at  the  normal  pressure  of  760  mm.  ? 
Ans.    15.18  oz. 

8.  Two  cubic  feet  of  air  expand  at  50°  F.  from  a  pressure 
of  80  pounds  to  a  pressure  of  60  pounds  by  the  gauge.     What 
is  the  external  work?     Ans.   6464  ft.  Ibs. 

9.  What  would  have  been  the  external  work  had  the  air 
expanded  adiabatically  ?     Ans.   4450  ft.  -Ibs. 

10.  Find  the  external  work  of  2   pounds  of  air  which  ex- 
pand  adiabatically   until   it  doubles    its    volume,    the    initial 
pressure  being  100  pounds  absolute  and  the  initial  tempera- 
ture 100°  F.     Ans.    36,100  ft.  -Ibs. 

11.  Find  the  external  work  of  one  kilogram  of  hydrogen 
which,  starting  with  the  pressure  of  4  atmospheres  and  with 
the   temperature  of   500°   C.,    expands  adiabatically   till    the 

perature  becomes  30°  C.     Ans.  489,280  m.-kg. 
2.   Find  the  exponent   for  an   exponential   curve  passing 
through   the   points/  =  30,   v  =  1.9,  and/,  =  15,  vl  =  9.6. 
Ans.  0.4279.    jf  •;  £- 


Jgp 
JM^ 
" 


PERFECT   GASES.  79 

13.  Find  the  exponent   for  a  curve   to  pass  through  the 
points/  =  40,  v  =  2,  and  pl  =  12,  vl  =  6.      Ans.    1.0959. 

14.  In  examples  2  and   3   let/  be  the  pressure  in  pounds 
on  the  square  inch  and  v  the  volume  in  cubic  feet.      Find  the 
external  work  of  expansion  in   each  case.      Ans.   21,900  and 
12,010  ft.-lbs. 

15.  Find   the   intrinsic   energy  of  one  pound   of  nitrogen 
under  the  standard  pressure  of  one  atmosphere  and  at  freezing- 
point  of  water.      Ans.   66,655  ft.-lbs. 

16.  A  pound  of  air  has  the  volume  6  cubic  feet  under  the 
pressure  of  30  pounds  absolute  to  the  square  inch.      Find  the 
intrinsic  energy.      Ans.   64,000  ft.-lbs. 

17.  In  example    16    find  the   increase   of    entropy  above 
that   at   atmospheric   pressure  and    at   freezing-point.      Ans. 
—  0.0516. 

1 8.  A  kilogram    of  oxygen  at  the  pressure  of  6   atmos- 
pheres and  at  100°  C.  expands  isothermally  till  it  doubles  its 
volume.      Find  the  change  of  entropy.      Ans.   40.0434. 

19.  Suppose   a   hot-air   engine,    in   which   the   maximum 
pressure   is  100  pounds  absolute,  and  the  maximum  temper- 
ature  is   600°    F.,    to   work  on  a    Carnot's  cycle.       Let   the 
initial  volume  be  2  cubic  feet,  let  the  volume  after  isothermal 
expansion   be   5   cubic  feet,   and   the  volume  after  adiabatic 
expansion  be  8   cubic  feet.      Find   the   external   work  of  one 
cycle ;   also   the  horse-power  if   the    engine   is   double-acting 
and   makes  30  revolutions  per  minute.      Ans.  8966  ft.-lbs., 
16.3  H.P. 


CHAPTER    VI. 
SATURATED   VAPORS. 

OUR  knowledge  of  the  properties  of  saturated  vapors  is 
derived  mainly  from  the  experiments  of  Regnault.*  In  most 
works  on  steam  and  other  vapors  the  results  of  his  experi- 
ments are  given  ,in  the  form  of  empirical  equations  designed 
to  be  used  for  calculating  tables  of  the  properties  of  vapors. 
Many  such  tables  have  been  calculated,  and  unfortunately 
they  show  such  diversity  of  values  as  to  lead  to  serious  incon- 
venience when  applied  in  practice.  It  therefore  appears 
advisable  to  give  the  original  data  on  which  the  empirical 
equations  are  based,  so  as  to  exhibit  the  limits  of  their 
application  and  the  degree  of  accuracy  to  be  attributed  to 
them.  The  constants  for  the  equations  for  calculating  the 
pressures  of  saturated  steam  at  different  temperatures  have 
been  recomputed  with  care  and  accuracy,  because  there  are 
minor  discrepancies  in  the  equations  given  by  Regnault. 
Rowland's  determinations  of  the  mechanical  equivalent  of  heat 
and  of  the  specific  heat  of  water  have  been  adopted,  and 
all  of  Regnault's  results  depending  thereon  have  been  revised 
and  brought  into  concordance  with  them. 

Pressure  of  Saturated  Vapor. — Regnault's  experiments 
on  the  temperature  of  saturated  vapor  consisted  essentially  in 
taking  the  temperature  of  the  boiling-point  of  the  vapor  under 
varying  pressures  of  the  atmosphere,  the  apparatus  being  so 
arranged  that  the  pressure  could  be  varied  from  a  small  frac- 
tion of  an  atmosphere  to  more  than  twenty  atmospheres. 

*  Mtmoires  de  r Institut  de  France,  etc.,  tome  xxvi. 

80 


SATURATED    VAPORS. 


8l 


The  temperature  was  taken  with  mercurial  thermometers, 
and  the  pressures  were  measured  by  a  mercury  column,  and, 
after  the  necessary  corrections  were  applied  and  temperatures 
were  reduced  to  the  air-thermometer,  Regnault  selected  the 
results  he  deemed  most  trustworthy,  and  plotted  a  series  of 
points,  and  then  drew  a  smooth  curve  to  represent  the  whole 
series  of  experiments. 

He  then  selected  points  on  the  experimental  curve  at  regu- 
lar intervals,  and  with  these  points  as  data  he  calculated  the 
constants  of  empirical  formulae  for  use  in  calculating  the 
tabular  values.  The  formula  selected  was  of  the  form 


log/  =  a  +  ban  -f-  c/3' 


(94) 


in  which  /  is  the  pressure,  and  n  is  the  temperature  minus 
the  constant  temperature  t9  of  the  lowest  limit  of  the  range  of 
temperature  to  which  the  formula  applies;  i.  e., 


Let  the  points  through  which  the  curve  represented  by 
the  equation  is  to  pass  be  (/„,  /,),  (/,,  /,),  (/,,  /,),  (/,,  /,), 
and  (/4,  /4),  so  chosen  that 


.-.   /,-/„  =  2(/I-/0),      (/,-/.)  =  3(',-/.),     (',-*.)  =  4(',-O- 
Substituting  the  five  known  values  of  p  and  t  in  equation  (94)  > 


l°g  A  =  *  +  b  +c'> 

log  /,  —  a  +  bo**  -'«     +  cfi**  -*°  ; 


log  A  =  a 
log  /4  =  a 


"•     •     •     (95) 


82  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Now  subtract  each  equation,  member  for  member,  from 
the  one  below  it,  and  for  convenience  let 


-  logA  =^0  >  etc-> 

-.     y^  =  (m   -      i) 
y,  =  (m*  -  -  m}b 


Solving    the    several    equations    for    c    and    equating   the 
values', 

j0  —  (m  —  i)b        y,  —  (m9  —  m)b 


(97) 


Again,  solving  for  b  and   equating  the  values  and  reduc- 
ing, 


n  —  m     ~  (n  —  m)m       (n  —  m)m*' 


wny*  —  0y,  —  ny*  — y*\ 

mny \  —  my^   =.  ny^  —  y^. 

mn  =  —         Hy^~y"~    =  ~          y    ^^    ;   •        ^8) 

m  +  n=  ^-ylyl  =  M' (99) 


SATURATED    VAPORS.  83 

Equations  (99)  and  ( I oo)  enable  us  to  calculate  numerically 
the  values  of  M  and  N  from  the  five  given  values  of  log  p. 
Then  solving  for  m  and  ny 


4 
Solving  one  of  the  equations  (97)  for  b, 

ny0  —  y  ny0  —  y 

==  ~( —   — ^ — ~r~* —  — \  ~~  ( —    — v Y     VIQI) 

Again,  solving  the  first  equation  of  (96)  for  c, 


(I02) 

**\*  *****  I 


•          x  \/  \ 

^  —  i  (»  —  i)(n  —  m) 

From  the  first  equation  of  (95) 

a  =  log/.  -  b  -  c  ........      (103) 


Finally,  a  =  m^  ~  '•  ;      .      ........     (104) 


(105) 


For  temperatures  below  freezing-point  Regnault  used  the 
equation 


/  =  a  -f-  ban, 


which  is  an  equation  to  a  curve  passing  through  three  points 
at  equidistant  temperatures,  and  of  which  the  solution  is  very 
simple. 


84  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Regnault's  Data  and  Equations  for  Steam. — For  equa- 
tion (106)  the  data  are: 

tt  =  —  32°  C.         /0  —  0.32  mm.  of  mercury. 
^  =  -  i6°C.         p^  =  1.29    "       " 
/a  =         o°C.         /2  =  4.6o    " 

From  which  Regnault  calculated  the  following  equation  by 
aid  of  seven-place  logarithms : 

A.   For  steam  from  —  32°  to  o°  C., 

p  =  a  -\-  ban; 

a  =  —  0.08038; 
log  b  —  9.6024724  —  10; 
log  a=  0.033398; 

n  =  32°  —  t. 

Regnault  uses  three  equations  of  the  form  given  by  equa- 
tion (97),  for  which  the  following  are  the  data: 

B. 


C. 


D. 


t,  =      o° 

C. 

A  = 

4.60  mm.  of  mercury. 

*,=  25° 

C. 

A  = 

23.55      "      " 

«« 

/.=  50° 

C. 

A  = 

91.98       "      " 

4< 

'.=    75° 

C. 

A  = 

288.50     "      " 

«* 

t,  =    100° 

C. 

A  = 

760           "      " 

i  < 

t.  =    100° 

C. 

A  = 

760            "      " 

it 

/,  =  130° 

C. 

A  = 

2030           "     " 

" 

/,  =  1  60° 

C. 

A  = 

4651.6        "      4< 

f4 

/3  =  190° 

C. 

A  = 

9426            4<      " 

t  < 

t.  =  220° 

C. 

A  = 

17390            ««      " 

" 

/.  =   -  20° 

C. 

A  = 

0.91      "     " 

« 

/,   =   +40° 

C. 

A  = 

54.91      »      - 

(1 

/,  =    100° 

C. 

A  = 

760            "      " 

« 

/,  =  1  60° 

C. 

A  = 

4651.6          **      " 

(  < 

/4  =  220° 

C. 

A  = 

17390            '*      «' 

•« 

SATURATED    VAPORS.  8$ 

And  from  these  data  he  calculated,  by  aid  of  seven-place 
logarithms,  the  following  equations,  which  are  correct  at  Paris: 

B.  For  steam  from  o°  to  100°  C., 

log  p  =  a  —  l>an  -J-  eft*  ; 

a  =  4.7384380; 
log  b  =  0.6116485  ; 
log   c  —  8.1340339  —  10  ; 
log  a  =  9.9967249  -  10 ; 
log  ft  =  0.006865036  ; 

n  =  /. 

C.  For  steam  from  100°  to  220°  C., 

log  p  =  a  —  hot*  -}-  eft*  ; 

a  =  5-4583895 ; 

log  b  =  0.4121470  ; 
log  c  =  7.7448901  —  ro  ; 
loga=  9.997412127  —  10  ; 
log  ft  =  0.007590697; 
n  =  t  —  100. 

D.  For  steam  from  —  20°  to  220°  C., 

log  /  =  a  —  ba*  —  eft*  ; 

a  —  6.2640348  ; 
log  b  =  0.1397743  ; 
log  c  =  0.6924351  ; 
log  a=  9.994049292  -  10 ; 
log/3  =  9.998343862  —  10  ; 

n  =  /  -j-  20. 

Regnault  gives  complete  tables  of  the  properties  of  satu- 
rated steam,  calculated  by  the  equations  just  set  down,  using 
equations  A  and  B  for  their  respective  ranges  of  temperature, 
but  he  uses  equation  D  (which  applies  to  the  entire  range 
from  —  20°  C.  to  -f-  120  C.)  instead  of  equation  C.  He  prob- 


86  THERMODYNAMICS   OF   THE   STEAM-ENGINE, 

ably  did  this  because  the  constants  calculated  for  equation  C 
with  seven-place  logarithms  are  unsatisfactory.  None  of  the 
constants  calculated  by  seven-place  logarithms  are  quite  satis- 
factory, for  two  places  of  significant  figures  are  unavoidably  lost 
in  the  calculation  of  tables;  one  place  is  lost  in  calculating 
the  constants,  and  one  is  lost  in  applying  the  equations,  leav- 
ing the  fifth  place,  which  should  appear  in  the  table,  subject 
to  error. 

Equations  for  the  Pressure  of  Steam  at  Paris. — In 
view  of  the  preceding  statements  it  appeared  desirable  to  re- 
calculate the  constants  for  equations  B  and  C  with  such  a 
degree  of  accuracy  as  to  exclude  any  doubt  as  to  the  relia- 
bility of  the  results.  Accordingly  the  logarithms  of  the  five 
values  of  /  for  each  equation  were  taken  from  Vega's  ten-place 
table,  and  then  the  remainder  of  the  calculations  were  carried 
on  with  natural  numbers,  checking  by  independent  methods, 
with  the  following  results  : 

B.  For  steam  from  o°  to  100°  C., 

log  /  =  a  —  ban  -f  cftn  ; 

a  —  4.7393622142 ; 
log    £  —  06117400190; 
log    c  —  8.1320378383  —  10  ; 
log  a—  9.996725532820  —  10  ; 
log  ft  —  0.006864675924  ; 

n  =  t. 

C.  For  steam  from  100°  to  220°  C., 

log  /  =  a  —  ban  -f-  cftn  ; 

«  =  5.4574301234 ; 
log   b  =  0.4119787931  ; 
log   c  =  7.7417476470  —  10  ; 
log  a=  9.99741106346  -  10  ; 
log  ft  =  0.007642489113  ; 
n  =  t  —  100. 

Pressure  of  Steam  at  Latitude  45°,  French  System.— 
It  is  customary  to  reduce  all  measurements  to  the  latitude  of 
45°  and  to  sea-level.  The  standard  thermometer  should 
then  have  its  boiling-  and  freezing-points  determined  under,  or 


SA  TURA  TED    VAPORS.  8/ 

reduced  to,  such  conditions.  The  value  of  g,  the  accelera- 
tion due  to  gravity  given  by  equation  (61),  139.809218  metres 
at  Paris,  latitude  48°  50'  14",  and  at  an  elevation  of  60 
metres.  At  45°  and  at  sea-level  £•—  9.806056;  consequently 
760  mm.  of  mercury  at  45°  latitude  give  a  pressure  equal  to 
that  of 

080.6056 
76ox  980.92  18  =  759.755™™. 

at  Paris,  and  by  equation  B  this  corresponds  to  a  temperature 
of  99°.  99  1  C.  In  other  words,  the  thermometer  which  is 
standard  at  45°  has  each  degree  0.99991  of  the  length  of  the 
degree  of  a  thermometer  standard  at  Paris. 

Again,  the  height  of  a  column  of  mercury  at  45°  latitude 

is  ,.  —  ^  times  the  height  of  a  column  which  will  give  the 

same  pressure  at  Paris.  Consequently  to  reduce  equation  B 
to  45°  latitude  we  have 


and  for  equation  C 

log  /  =  a  +  log  -  ^(°-99991  '  -  I00) 


=    a  -4-   log  '  -  bOi  ~  °-oo9*o.999K/  -  .00) 

5    980.6056 


~  0.009  ff-9999i(*  -  loo). 


The  resulting  equations  are  : 

B.   For  steam  from  o°  to  100°  C.  at  45°  latitude, 


«i  =  4.7395022; 
log  b  =  0.6117400190; 
log  c  =  8.1320378383  -  10; 


88  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

log  or,  =:  9.996/25827522  —  10  ; 
log/?,  =  0.006864058103  ; 
n  —  t. 

C.   For  steam  from  100°  to  220°  C.  at  45°  latitude, 

log  p  —  a,  —  b^a?  +  <:,/?,"  ; 

a,  =  5-457570I; 
log^  =  0.4120020935  ; 
log  cv  =  7.7416788646  —  10 ; 
log  cxl  =  9.99741 1296464  —  10; 
log  fa  —  0.007641801289; 
n  —  t  —  100. 

Pressure  of  Steam  at  Latitude  45°.  English  System.— 
To  reduce  the  equations  for  the  pressure  of  steam  so  that 
they  will  give  the  pressures  in  pounds  on  the  square  inch  for 
degrees  Fahrenheit  there  are  required  the  comparison  of 
measures  of  length  and  of  weight,  the  comparison  of  the  scales 
of  the  thermometers,  and  the  specific  gravity  of  mercury. 

Professor  Rogers  *  gives  for  the  length  of  the  metre  39. 3702 
inches.  This  differs  from  the  value  given  by  Captain  Clarke  f 
by  an  amount  that  does  not  affect  the  values  in  the  tables, 
his  value  being  39.370432  inches. 

Professor  Miller  \  gives  for  the  weight  of  one  kilogram 
2.20462125  pounds. 

Regnault  §  gives  for  the  weight  of  one  litre  of  mercury 
J3-5959  kilograms. 

The  degree  Fahrenheit  is  -|  oi  the  degree  centigrade. 

Let  k  =  13'59jg  X  2'2°4621  . 

39-37021 


*  Proceedings  of  the  Am.  Acad.  of  Arts  and  Sciences,  1882-83;  also  addi- 
tional observations. 

f  Proceedings  of  the  Royal  Society,  vol.  xv,  1866. 
J  Philosophical  Transactions,  cxlvi,  1856. 
>§  Me'moires  de  V  Institut  de  France,  vol.  xxi. 


SATURATED    VAPORS.  89 

then  equations  B  and  C  have   for  the  reduction  to  degrees 
Fahrenheit,  and  pounds  on  the  square  inch, 

log/  =  a,  +  log  k  -  b<x*«  +  cftf; 
log/  =  a,  +  log  k  -  b,a*  +  cjf. 
The  resulting  equations  are  : 

B.  For  steam  from  32°  to  212°  F.  in  pounds  on  the  square 
Inch, 

log  /  =  a,  —  ba?  +  cpf  ; 

a,  =  3.025908; 
log  b  =  0.6117400; 
log  c  =  8.13204  —  10; 
logo',  =  9.998181015  —  10; 
log  £,=  0.0038  1  34; 
n  —  t  —  32. 

C.  For  steam  from  2  12°  to  428°  F.  in  pounds  on  the  square 
inch, 


«,  =  3-743976; 
=  0.4120021  ; 

log  c,  =  7.74168  —  10; 
logo-,  =  9.998561831  —  10; 
log  A  =  0.0042454; 
n   =  t  —  212. 

Other  Equations  for  the  Pressure  of  Steam.—  A  num 
her   of  other  forms   have    been  proposed    for  the  empirical 


90  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

equations  for  calculating  the  pressure  of  saturated  steam  ;    one 
of  the  best  is  that  given  by  Rankine  *  having  the  form 


(107) 


Assuming  the  absolute  zero  on  the  Fahrenheit  scale  to  be 
at  —  461°. 2,  he  computed  for  pressure  on  the  square  inch  the 
following  values  for  his  constants : 

A  =6.1007;     log  £=  3.43642;     log  C=  5. 59873- 

This  equation  has  the  advantage  that  it  may  be  solved 
directly  for  T,  a  property  that  Regnault's  equations  do  not 
have.  It  gives  fairly  accurate  results,  and  the  greater  part  of 
English  tables  of  properties  of  saturated  steam  are  calculated 
by  its  aid. 

A  number  of  exponential  formulae  have  been  devised,  of 
which  the  principal  advantage  is  the  facility  of  application. 
The  following,  by  Magnus,  gives  pressures  in  mm.  of  mercury 
for  degrees  centigrade,  and  agrees  quite  well  with  Regnault's 
results  below  100°,  but  is  not  so  correct  above  100°  : 

7-4475* 

p  =  4-525  X  10234.69  +  * (108) 

Pressure  of  Other  Vapors. — Regnault  f  determined  also 
the  pressure  of  a  large  number  of  saturated  vapors  at  various 
temperatures,  and  deduced  equations  for  each  in  the  form  of 
equation  (94).  The  equations  and  the  constants  as  deter- 
mined by  him  for  the  commoner  vapors  are  given  in  the  fol- 
lowing table : 


*  Steam-engine  and  Other  Prime  Movers. 

\  Acade'tnie  des  Sciences,  Comptes  rent/us,  tome  xxxvi. 


SATURATED    VAPORS. 
PRESSURE  OF  SATURATED  VAPORS. 


91 


log 

P 

a 

b 

c 

Alcohol    

,1 

fer» 

5.4562028 

4.9809960 

0.0485397 

Ether  

d 

4-  ban 

—  c6n 

5.0286298 

O.OOO2284 

3.1906390 

Chloroform  

a 

—  bcx.n 

—  c6» 

2  0^-31281 

0.0668673 

Carbon  bisulphide.... 
Carbon  tetrachloride.  . 

a 
a 

—  ban 
—  ba* 

-ej3" 

5.4OII662 
12.0962331 

3.4405663 
9.I375I80 

0.2857386 
1.9674890 

log  a 

log/3 

- 

Limits. 

Alcohol 

T.QQ7o8tiI>7 

Q4.OQJ.8^ 

t  -}-  2O 

—  20°   -f-  i  ^o°  C 

Ether  

o  014^775 

000877 

/  4-  20 

—   20°    -(-  I2O°  C 

Chloroform  
Carbon  bisulphide.... 
Carbon  tetrachloride.. 

1.9974144 
1.9977628 
1.9997120 

.9868176 
.9911997 
.9949780 

/  —   20 
/+  20 
/  +  20 

4-  20°,  +  164°  C. 
—  20°,  -f-  140°  C. 
-  20°,  -f  188°  C. 

Zeuner*  states  that  there  is  a  slight  error  in  Regnault's  cal- 
culation of  the  constants  for  aceton,  and  gives  instead 

log     p  =  a  —  ban  -|-  cftn : 

a  =  5.3085419; 

log  botn  =  +  0.5312766  —  0.0026148^; 
log  cfin  =  —  0.9645222  —  0.02I5592/. 

Differential  Coefficient  ^. — From   the  general  form  of 
the  equation  (94)  we  have 


—c/3*,       ,      .      (109) 


M  being  the  modulus  of  the  common  system  of  logarithms. 
Differentiating, 


*Mechanische  Warmetheorie. 


92  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

or,  reducing  to  common  logarithms, 


_  <^_    +  Bfin (no) 

p  dt 

For  saturated  steam  at  45°  latitude  the  constants  to  be 
used  with  equation  (no)  are: 

French  units. 

B.  For  o°  to  100°  C.,  mm.  of  mercury, 

log  A  =  8.85  12729  —  io; 
log  B  =  6.69305  —  io; 
log  ofl  =  9.996725828  —  io; 
log  /?,  =  0.0068641. 

C.  For  100°  to  220°  C.,  mm.  of  mercury, 

log  A  =  8.5495158-  io; 
log  B  —  6.34931  —  io ; 
logo',  =  9.997411296—  io; 
log/?,  —  0.0076418. 

English  units. 

B.  For  32°  to  212°  F.,  pounds  on  the  square  inch, 

log  A  —  8.5960005  —  io; 
log  B  —  6.43778  —  io; 
log  «,  =  9.998181015  —  io- 
log/?,  =  0.0038134. 

C.  For  212°  to  428°  F.,  pounds  on  the  square  inch, 

log  A  =  8.2942434-  io ;  % 
log  B  =  6.09403  —  io; 
log  a,  =  9.998561831  —  io; 
log/?,  =  0.0042454. 


SATURATED    VAPORS. 


93 


It  is  to  be  remarked  that  -f  may  be  found  approximately 

at 

by  dividing  a  small  difference  of  pressure  by  the  corresponding 
difference  of  temperature  ;  that  is,  by  calculating  —  .  With  a 

table  for  even  degrees  of  temperature  we  may  calculate  the 
value  approximately  for  a  given  temperature  by  dividing  the 
difference  of  the  pressures  corresponding  to  the  next  higher  and 
the  next  lower  degrees  by  two. 

The  following  table  of  constants  for  the  several  vapors 
named  were  calculated  by  Zeuner  from  the  preceding  equa- 
tions for  temperature  and  pressure  of  the  same  vapors  : 


DIFFERENTIAL   COEFFICIENT    -  -. 

dt 


SIGN. 

log  (A  a11) 

log  (2?/3*) 

Aa» 

BfP 

Alcohol  

+-H-+++ 

—     .1720041  —  0.0029143* 
—     .3396624  —  0.0031223* 
—     .3410130  —  0.0025856* 
—     -4339778  —  0.0022372* 
—     .8611075  —  0.0002880* 
—     .3268535  —  0.0026148* 

—  2.9992701  —  0.0590515* 
—  4.4616396  -|-  0.0145775* 
—  2.0667124  —  0.0131824* 
—  2.0511078  —  0.0088003* 
—  1.3812195  —  0.0050220* 
—  1.9064582  —  0.0215592* 

Ether                   

Carbon  bisulphide  
Carbon  tetrachloride  — 

Rowland's  Experiments. — The  most  accurate  and  re- 
liable determinations  of  the  mechanical  equivalent  of  heat 
were  made  by  Rowland,*  who  found  that  there  is  a  notable 
variation  of  the  mechanical  equivalent  at  low  temperatures. 
His  experiments  give  a  very  delicate  determination  of  the 
specific  heat  of  water  at  low  temperatures,  and  consequently  of 
the  heat  of  the  liquid,  i.e.,  the  heat  required  to  raise  water 
from  freezing-point  to  a  given  temperature. 

The  apparatus  used  was  similar  to  that  used  by  Joule,  with 
modifications  to  give  greater  certainty  of  results.  The  calo- 
rimeter was  of  larger  size,  and  the  paddle  had  the  upper  vanes 
curved  like  the  blades  of  a  centrifugal  pump,  to  give  a  strong 


*  Proceedings  of  the  American  Academy,  vol.  xv  (N.  S.  vii),  1879. 


94  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

circulation  up  through  the  centre,  past  the  thermometer  for 
taking  the  temperatures,  and  down  at  the  outside.  The  paddle 
was  driven  by  a  petroleum-engine,  and  the  power  applied  was 
measured  by  making  the  calorimeter  into  a  friction-brake,  with 
two  arms  at  which  the  turning  moment  was  measured.  Radia- 
tion was  made  as  small  as  possible,  and  then  was  made  deter- 
minate by  use  of  a  water-jacket  outside  of  the  calorimeter. 

The  experiments  consisted  essentially  in  delivering  a  meas- 
ured amount  of  work  to  the  water  in  the  calorimeter  and  in 
measuring  the  rise  of  temperature  due  to  it.  The  whole 
range  of  experiments  was  from  2°  to  41°  C.  It  is,  however, 
convenient  to  make  our  calculations  of  the  properties  of 
saturated  steam  and  of  water  begin  at  freezing-point ;  conse- 
quently for  this  purpose  it  has  been  assumed  that  the  mechani- 
cal equivalent  of  heat  is  constant  from  freezing-point  to  3°  C. 
The  work  required  to  raise  one  kilogram  of  water  from  2°  to 
3°  is  430  metre-kilograms,  so  that  our  assumption  gives  for  the 
work  required  to  raise  one  kilogram  of  water  from  freezing- 
point  to  3°,  1290  metre-kilograms.  Any  error  that  may  come 
from  this  assumption  is  eliminated  in  practical  calculations,  for 
we  always  deal  with  differences  of  the  heat  of  the  liquid,  and 
seldom  or  never  have  a  temperature  so  low  as  2°  C.  With  the 
assumption  just  made  Rowland's  experiments  may  be  ex- 
pressed by  the  table  on  page  95. 

In  column  2  is  given  the  work  in  metre-kilograms  required 
to  raise  one  kilogram  of  water  from  freezing-point  to  the  tem- 
perature given  in  column  I,  while  column  3  gives  the  most 
probable  mechanical  equivalent  of  heat  for  the  several  tempera- 
tures from  5°  to  36°  C.  The  other  two  columns  will  be  dis- 
cussed under  the  head  of  Specific  Heat  of  Water. 

Standard  Temperature. — In  the  beginning  of  our  work 
it  was  stated  that  we  should  use  62°  F.  for  our  standard  tem- 
perature; and  the  reasons  for  so  doing  may  now  be  shown. 
We  know  actually  nothing  about  the  specific  heat  of  water 
from.  o°  to  2°  C. ;  consequently  the  commonly  accepted  value 
of  the  thermal  unit — i.e.,  the  heat  required  to  raise  one  unit 


SATURATED    VAPORS.  95 

ROWLAND'S    MECHANICAL   EQUIVALENT   OF    HEAT. 


I      » 

^ 

x~~ 

"j3 

S       <« 

^ 

x-J 

"5 

u 

8 

1 

-°    s 
ial 

*22f 

1*3 

ill 

«ja"o 

3flJ 

WT3   «» 

ill 

ij  s. 

4 

2  'IS 

rt  "t  3 
(Ui—  1  y 

u 

t> 

Isl 

?*I 

c  cUi 

Ija 

c  >  w 

l'§5 

«5w^ 

gl 

Bl 

s^s. 

Si 

4-1     tT       * 

rt  "\  3 

fc-t  -j 

P 

H 

5S 

X 

EC 

p 

H 

s 

» 

1 

3 

4 

5 

I 

2 

3 

4 

5 

4^O 

1.0068 

i  .007 

22 

0424 

426.1 

22.065 

22.063 

2 

'tjv-' 
860 



2.0135 

X    .  \J**J  J 

2.014 

23 

yr**f 
9850 

426.0 

23-063 

23.061 

I2OO 

o    Q2O4 

"1.022 

24 

IO277 

425  .9 

24.062 

24.059 

L^^-> 

1721 

J  •  v-'^*-w^ 

4.O2Q5 

o  .  *-'*•*• 

4.O2Q 

25 

IO7OI 

•T^*  j  v 
425.8 

25.055 

25.058 

5 

L  j  AL 
2150 

429.8 

.  \j&\.j3 
5-0339 

H-  *  *~"'^j 
5.036 

26 

III28 

425.7 

26.054 

26.053 

6 

2580 

6.0408 

6.O4O 

27 

U553 

425-6 

27.050 

27  .  048 

7 

3009 

429-3 

7-0452 

7-045 

28 

II978 

425-6 

28.045 

28.042 

8 

3439 

429.0 

8.0520 

8.049 

29 

12399 

425.5 

29.031 

29.037 

9 

3868 

428.8 

9.0564 

9-054 

30 

12828 

425-6 

30-035 

30.032 

10 

4296 

428.5 

IO.O59 

IO.O58 

31 

13253 

425-6 

31.030 

31-027 

ii 

4723 

428.3 

11.058 

II.  000 

32 

136/5 

425-6 

32.018 

32.023 

12 

428.1 

12.061 

12.061 

33 

I4IOI 

425-7 

33.016 

33-oiS 

13 

5578 

427.9 

13.060 

13.063 

34 

I452/ 

425   7 

34-OH 

34  014 

*4 

6006 

427-7 

14.063 

14.064 

35 

M952 

425.8 

35.008 

35.009 

15 

6433 

427.4 

15.065 

15.066 

36 

15379 

425-8 

36.008 

36-007 

16 

4.27    2 

1  6  00*1. 

16.066 

07 

T  "  ^  <    " 

•17   007 

37  .  005 

1  U 

f  -7 

Q1 

/I  O"7    O 

17.066 

17.066 

ji 

08 

16231 

j  1  •*-"-'/ 
38.003 

18  004 

A  / 

18 

7717 

4^/  •  u 

426.8 

i8.'o68 

18.066 

ju 
39 

16657 



39.000 

j*-*  -  v^-'4t- 
39.002 

19 

8144 

426.6 

19.068 

19.066 

40 

17083 

...    . 

39.998 

40.000 

20 

8571 

426.4 

20.068 

20.066 

41 

17508 



40-993 



21 

8997 

426.2 

21.065 

21.064 

of  weight  of  water  from  o°  to  i°  C.,  or  from  32°  to  33°  F. — is 
an  ideal  quantity  inferred  from  the  behavior  of  water  at  higher 
temperatures.  It  is  more  scientific  to  take  an  easily  verified 
quantity  for  the  standard;  and  there  is  a  practical  convenience 
in  choosing  62°  F.  for  the  standard  temperature,  because  it  is 
near  the  mean  temperature  of  the  air  during  experimental 
work.  Therefore  it  is  near  the  mean  temperature  in  the 
calorimeter  during  ordinary  work  with  that  instrument;  and 
the  specific  heat  of  water  for  the  range  of  temperature  in  the 
calorimeter  may  usually  be  considered  to  be  unity,  without 
error,  unless  great  refinement  is  desired.  Moreover,  62°  F. 
is  the  temperature  at  which  the  English  units  of  weight  and 
measure  are  standard. 

Mechanical  Equivalent  of  Heat. — 62°  F.  corresponds 
with  i6f°  C.,  at  which  the  mechanical  equivalent  of  heat  given 


THERMODYNAMICS    OF    THE   STEAM-ENGINE. 


in  the  table  of  Rowland's  experiments  is  427.1.  The  value 
of  g  at  Baltimore,  latitude  39°  17',  is  980.05  centimetres; 
therefore,  reducing  to  45°  of  latitude,  where  g  —  980.6056 
centimetres,  the  value  of/  is 


/=  427.1  X 


980  05 


=  426.9  metre-kilograms. 


To  reduce  to  the  English  system  of  units  it  is  sufficient  to 
multiply  by  f  ,  giving 

J  =  778  foot-pounds. 

Since  the  value  given  by  Joule  is  commonly  quoted,  it 
will  be  of  interest  to  make  a  comparison  of  his  latest  work 
(1873)  with  Rowland's,  as  given  in  the  following  table: 

COMPARISON    OF    ROWLAND'S    AND    JOULE'S    EXPERIMENTS. 


Reduced  to  the  Air-thermometer 

Temperature. 

Joule's  Value  at 
Manchester, 
English  System. 

and  to  the  Latitude  of  Baltimore. 

Rowland's  Value 
Corresponding. 

English. 

French. 

I2°.7 

774.6 

778.5 

427.1 

428.0 

14  -5 

767.0 

770.5 

422.7 

427.6 

14  .7 

772.7 

776.1 

425-8 

427.5 

15  -5 

773-1 

776.4 

426.0 

427.3 

17  -3 

774-0 

777-0 

426.3 

426.9 

Specific  Heat  of  Water. — From  freezing-point  to  40°  C. 
the  specific  heat  of  water  may  be  determined  from  Rowland's 
experiments  on  the  mechanical  equivalent  of  heat  as  arranged 
in  the  table  on  page  95.  For  this  purpose  we  may  first  divide 
the  metre-kilograms  required  to  raise  one  kilogram  of  water 
from  freezing-point  to  a  given  temperature,  as  set  down  in 
column  2  of  that  table,  by  the  mechanical  equivalent  of  heat 
(427.1  kilograms)  at  the  latitude  of  Baltimore.  This  gives 
the  experimental  values  of  the  heat  of  the  liquid  given  in 
column  4.  This  column  shows  some  accidental  experimental 
irregularities,  which  were  eliminated  by  drawing  a  diagram 


SATURATED    VAPORS. 


97 


with  temperatures  for  abscissae  and  with  heats  of  the  liquid 
for  ordinates.  That  diagram  also  made  it  possible  to  assign 
the  series  of  values  of  the  specific  heat  of  water  from  freezing- 
point  to  40°  C.  given  is  the  following  table : 

SPECIFIC    HEAT   OF   WATER. 


RANGE. 

Specific  Heat. 

Centigrade. 

Fahrenheit. 

o  to       5 

32    to      41 

I  .0072 

5  to     10 

41    to     50 

1.0044 

10  to     15 

50  to     59 

I.  0016 

15  to     20 

59  to     68 

I. 

20    to      25 

68  to     77 

0.9984 

25   to     30 

77  to     86 

0.9948 

30  to     35 

86  to     95 

0.9954 

35  to     40 

95  to  104 

0.9982 

40  to     45 

104  to  113 

I. 

45   to  155 

113  to  311 

1.008 

155   to  200 

311   to  392 

1.046 

The  calculated  heats  of  the  liquid  given  in  column  5  of  the 
table  on  page  95  were  calculated  with  the  specific  heats  in 
the  above  table.  They  are  more  regular  than  the  quantities- 
in  the  4th  column,  and  differ  from  them  no  more  than  can 
properly  be  attributed  to  accidental  irregularities. 

For  the  heat  of  the  liquid  and  the  specific  heat  of  water 
beyond  40°  C.  it  is  necessary  to  go  to  Regnault's  determina- 
tions. Having  satisfied  himself  that  the  specific  heat  of  water 
at  low  temperatures  was  practically  constant,  Regnault  pro- 
ceeded to  determine  the  specific  heat  of  water  at  high  tem- 
peratures by  the  method  of  mixtures,  running  hot  water  from 
the  water-space  of  a  boiler  into  a  calorimeter  containing  cold 
water.  The  record  of  his  work  gives  forty  such  tests.  To 
prepare  these  tests  for  our  purposes  it  was  necessary  to  cor- 
rect his  calculations  for  the  true  specific  heat  of  the  water  ire 
the  calorimeter;  after  this  was  done  the  true  heat  of  the  liquid 
was  readily  determined  and  was  plotted  on  the  same  diagram 
with  the  heats  of  the  liquid  from  Rowland's  work,  and 


98  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

specific  heats  for  water  from  40°  to  45°,  from  45°  to  155°,  and 
from  155°  to  200°,  centigrade,  were  assigned  as  given  in  the 
.above  table  of  the  specific  heats  of  water. 

It  is  interesting  to  know  in  this  connection  that  after  his 
investigation  of  the  mechanical  equivalent  of  heat  and  the 
^consequent  determination  of  the  specific  heat  of  water 
Rowland  repeated  Regnault's  experiments  on  the  specific 
Jieat  of  water  at  low  temperatures  by  the  method  of  mixtures, 
and  that  he  found  it  possible  to  recognize  the  very  peculiar 
behavior  of  water  at  low  temperatures,  which  is  so  clearly 
shown  by  his  experiments  recorded  in  the  table  on  page  95  ; 
but  his  work  showed  that  the  unavoidable  irregularities  of  the 
method  of  mixtures  were  a  large  part  of  the  differences 
between  the  true  specific  heat  and  unity,  which  shows  why 
Regnault  failed  to  find  any  variation  in  the  specific  heat  of 
water  at  low  temperatures. 

In  using  the  specific  heats  of  water  for  calculating  the  heat 
of  the  liquid  by  aid  of  the  table  on  page  97  it  is  necessary 
to  proceed  step  by  step.  Thus  the  heat  of  the  liquid  at 
23°  C.  is 

5  X  1.0072  +  5X1.0044  +  5  X  1.0016  +  5  X  i  +  3  X  0.9984 

=  23.061  B.  T.   U. 

Specific  Heat  of  Other  Liquids. — Regnault  determined 
the  specific  heats  and  the  heats  of  the  liquid  of  various  other 
liquids  besides  those  for  water,  using  the  method  of  mixtures 
for  all  his  work.  The  following  table  gives  his  results  un- 
altered : 

HEAT   OF   THE    LIQUID. 
Alcohol q  —  0.54754;?  -j-  0.0011218^ 

-j-  O.OOOOO22O6/3 

Ether q  =  0.52901^  +  0.0002959^ 

Chloroform - q  =  0.23235^  -(-  0.0000507^ 

Carbon  bisulphide q  =  0.23523^  -f  0.00008 is/'2 

Carbon  tetrachloride q  =  o.  igjgSf  -\-  o.oooogo6/2 

Aceton q  =  0.50643^  +  o.ooo396s/2 

Water q  —  t  -\-  o.oooo2/--f-  o.oooooos/3 


SATURATED    VAPORS.  99 

Regnault's  equation  for  water  is  included  here  to  make 
his  work  complete;  it  of  course  gives  very  different  results 
from  those  by  the  table  of  specific  heats  on  page  97. 

The  specific  heat  for  any  liquid  may  be  determined  at  any 
temperature  by  differentiating  the  corresponding  equation  for 
the  heat  of  the  liquid.  Thus  Regnault's  equation  for  the 
specific  heat  of  water  is 

da 
c  =  -r  =  i  +  o.oooc>4/  +  0.0000009/5. 

Total  Heat. — This  term  is  defined  as  the  heat  required  to 
raise  a  unit  of  weight  of  water  from  freezing-point  to  a  given 
temperature,  and  to  entirely  evaporate  it  at  that  temperature. 
The  experiments  made  by  Regnault  were  in  the  reverse  order; 
that  is,  steam  was  led  from  a  boiler  into  the  calorimeter  and 
there  condensed.  Knowing  the  initial  and  final  weights  of 
the  calorimeter,  the  temperature  of  the  steam,  and  the  initial 
and  final  temperatures  of  the  water  in  the  calorimeter,  he  was 
able,  after  applying  the  necessary  corrections,  to  calculate  the 
total  heats  for  the  several  experiments. 

As  a  conclusion  of  the  work  he  gives  the  following  values 
for  the  total  heats: 

10° 610     By  equation,  609.6 

63° 625  625.2 

100°. 637 

195° 666 

Assuming  an  equation  of  the  form 

\  =  A+Bt, (in) 

Regnault  calculated  the  constants  from  the  values  given  for 
100°  and  195°,  and  gives  the  equation 

X  =  606.5  -f-0.305/ (112) 


100  T  HER  MOD  YNAMICS   OF   THE   STEAM-ENGINE. 

An  investigation  of  the  original  experimental  results, 
allowing  for  the  true  specific  heat  of  the  water  in  the  calo- 
rimeter, showed  that  the  probable  errors  of  the  method  of 
determining  the  total  heat  were  larger  than  the  deviations 
of  the  true  specific  heats  from  unity,  the  value  assumed  by 
Regnault;  and,  further,  it  appeared  that  his  equation  repre- 
sents our  best  knowledge  of  the  total  heat  of  steam.  The 
probable  error  appears  to  lie  between  ToVo  an<^  TrJir*  making 
the  total  heat  the  most  uncertain  of  the  experimental  proper- 
ties of  steam. 

For  the  Fahrenheit  scale  the  equation  becomes 

V 


Ji=  1091.7  +  0.305^-  32).  ~.      .      .      (113) 

Regnault  gives  the  equations  following  for  other  liquids: 

Ether  ...............   A  =    94     +0.45^        —  0.0005  55  56** 

Chloroform  .........   A  =     67     -f-  0.1375^ 

Carbon  bisulphide...   A  =    90      -f-  0.14601^  —  0.0004123^ 
Carbon  tetrachloride  A  —     52      +  0.14625^  —  o.oooi72/2 
Aceton  ..............  A  =  140.5  -f-  0.30644^  —  0.0005  16/2 

Heat  of  Vaporization.  —  If  the  heat  of  the  liquid  be  sub- 
tracted from  the  total  heat,  the  remainder  is  called  the  heat 
of  vaporization,  and  is  represented  by  r,  so  that 


(114) 


Specific  Volume  of  Liquids.  —  The  coefficient  of  expan- 
sion of  most  liquids  is  large  as  compared  with  that  of  solids, 
but  it  is  small  as  compared  with  that  of  gases  or  vapors. 
Again,  the  specific  volume  of  a  vapor  is  large  compared  with 
that  of  the  liquid  from  which  it  is  formed.  Consequently  the 
error  of  neglecting  the  increase  of  volume  of  a  liquid  with  the 
rise  of  temperature  is  small  in  equations  relating  to  the  ther- 
modynamics of  a  saturated  vapor,  or  of  a  mixture  of  a  liquid 
and  its  vapor  when  a  considerable  part  by  weight  of  the  mix- 
ture is  vapor.  It  is  therefore  customary  to  consider  the 
specific  volume  of  a  liquid  <r  to  be  constant. 


SATURATED    VAPORS. 


101 


The  following  table  gives  the  specific  gravities  and  specific 
volumes  of  liquids: 
SPECIFIC    GRAVITIES   AND    SPECIFIC   VOLUMES    OF   LIQUIDS. 


Specific 
Gravity, 
compared 
with  Water 
at  4°  C. 

Specific  Volume. 

Cubic  Metres. 

Cubic  Feet. 

0.80625 
0.736 
I-527 
1.2922 
1.6320 
0.81 

1-433^ 
0.6364 
i 

0.001240 
0.001350 
0.000655 
0.000774 
0.00613 
0.00123 
0.0006981 
0.001571 
O.OOI 

O.OII2 
0.0252 
O.OI6O2 

Ether     

Sulphur  dioxide  -  

Water    

Experiments  were  made  by  Hirn  *  to  determine  the 
volumes  of  liquid  at  high  temperatures  compared  with  the 
volume  at  freezing-point,  by  a  method  which  was  essentially 
to  use  them  for  the  expansive  substance  of  a  thermometer. 
The  results  are  given  in  the  following  equations: 
SPECIFIC  VOLUMES  OF  HOT  LIQUIDS. 


Logarithms. 

Water, 

100°  C.  to  200°  C. 

(Vol.  at  4°  =  unity.) 

v  =  i  +  o.oooio867875/ 
4-  o.ooooo3oo73653/i 
-j-  0.00000002  8  7  3042  2^ 
—  0.0000000000066457031^ 

6.0361445  —  10 
4.4781862  —  10 
1.4583419  —  10 

8.8225409  —  20 

Alcohol, 
30°  C.  to  160°  C. 
(Vol.  at  o°  =  unity.) 

v  =  i  -f-  0.00073892265/ 
-j-  0.00001055235^ 
—  o.ooooooo9248oS4223 
-f-  0.0000000004041  3567^ 

6.8685991  —  10 
3.0233492  —  10 
2.9660517  —  10 
0.6065278  —  10 

Ether, 

30°  C.  to  130°  C. 
(Vol.  at  o°  =  unity.) 

v  =  I  +  O.OOI3489059/ 
-j-  0.0000065  5  3  7/2 
—  0.0000000344907  5  6/3 
4-  0.00000000033  7  72062/4 

7.1299817  —  10 
4.8164866  —  10 
2.5377028  —  10 
0.5285571  —  10 

Carbon  Bisulphide, 
30°  C.  to  160°  C. 
(Vol.  at  o°  =  unity.) 

v  —  i  -J-  0.0011680559* 
-j-  0.0000016489598^ 
—  0.0000000008  1  1  19O62/3 
-f-  o.  0000000000609465  89** 

7.0674636  —  10 
4.2172103  —  10 
0.9091229  —  10 

9.7849494  —  20 

Carbon  Tetrachloride, 
30°  C.  to  160°  C. 
(Vol.  at  o°  =  unity.) 

v  =  i  -f-  o.ooio67i883/ 
-j-  0.000003565  1  378^ 
—  0.00000001494928  1/3 
-|-  0.000000000085  1  823  iS*4 

7.0282409  —  10 
4.5520763—  10 
2.1746202  —  10 

9.9303494-20 

*  Annales  de  Chimie  et  de  Physique,  1867. 


102  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Internal  and  External  Latent  Heat. — The  heat  of 
vaporization  overcomes  external  pressure,  and  changes  the 
state  from  liquid  to  vapor  at  constant  temperature  and  pres- 
sure. Let  the  specific  volume  of  the  saturated  vapor  be  s 
and  that  of  the  liquid  be  <r;  then  the  change  of  volume  is 
s  —  cr  —  u  on  passing  from  the  liquid  to  the  vaporous  state. 
The  external  work  is 

/(*-  <r)=/«,     -     -    -\     -      •      (US) 

and  the  corresponding  amount  of  heat,  or  the  external  latent 
heat,  is 

Ap(s  —  a)  =  Apu.  .     ...      .     (116) 

The  heat  required  to  do  the  disgregation  work,  or  the 
internal  latent  heat,  is 

p=  r  —  Apu.  .     .     .     .          .     (117) 

General  Equation. — A  pound  or  a  kilogram  of  a  mixture 
of  a  liquid  and  its  vapor  consists  of  a  certain  part,  x,  of 
vapor,  and  the  remainder,  I  —  x,  of  liquid.  The  specific 
volume  of  the  mixture  is 

v  —  xs  -f-  (i  —  x)<r  =  (s  —  <?}x  +  0"  =  ux  -f-  cr,       (i  18) 

in  which  s  is  the  specific  volume  of  saturated  vapor,  cr  is  the 
specific  volume  of  the  liquid,  and  u  is  the  increase  of  volume 
due  to  vaporization. 

Since  the  pressure  of  saturated  vapor  depends  on  the  tem- 
perature only,  the  variables  in  the  general  equation  for  a  mix- 
ture of  a  liquid  and  its  vapor  are  temperature  and  volume; 
and  the  specific  volume  as  shown  by  equation  (118)  depends 
upon  x,  the  condition  of  the  mixture,  and  on  s  or  u,  which  in 
turn  depend  on  the  temperature  only.  Consequently  the 
general  equation  may  be  expressed  as  a  function  of  t  and  x. 

When  a  mixture  of  liquid  and  its  vapor  receives  heat 
there  is  in  general  an  increase  in  the  temperature  of  the  por- 
tion x  of  vapor  and  in  the  portion  i  —  x  of  liquid,  and  there 


SATURATED    VAPORS.  IO3 

is  a  vaporization  of  part  of  the  liquid.  Taking  c  for  the 
specific  heat  of  the  liquid  and  h  for  the  specific  heat  of  the 
vapor,  while  r  is  the  heat  of  vaporization,  we  shall  have  for 
an  infinitesimal  change 


dQ  =  hxdt  +  c(i  —  x)dt  +  rdx.        .      .     (119) 

Application  of  the  First  Law.  —  The  first  law  of  ther- 
modynamics is  applied  to  equation  (119)  by  combining  it  with 
equation  (23),  so  that 

dQ  =  A(dE  +  pdv)  =  hxdt  +  c(i  -  x)dt  +  rdx  ;    (120) 
.-.     dE  =  ±[/ix  +  c(i  -  xfidt  +  ^dx  -  pdv.    .     .     (121) 

But       *= 


d*E 

Since 


,     ,  , 

dx  dt       dt  dx 

d 


Bearing  in  mind   that  //,  c,  and  /  are  functions  of   /,  and 
not  of  x,  the  differentiation  gives 

I  ,  d*v  I  dr       dptdv\  d*v 


Since/  and  r  are  functions  of  £,  and  not  of  x,  the  expres- 

dr          dp  idr\  idp\ 

sions  -j-  and  -77  are  written  instead  of  f-j-     and  l-f    .     From 
dt          dt  \dtjx          \dtjx 

equation  (118)  we  have  (<r  being  constant) 


104          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and,  further,  we  have 

d*v          d^v 
dx  dt  ~  dtdx' 

so  that  equation  (123)  reduces  to 


(124) 


dQ 
Application  of  the  Second  Law.  —  By  this  law  -=-  is  an 


exact  differential. 

dQ 


.     (125) 


T5..X.  ^    ^        or 

~" 


dt  dx  dx  dt  dt  dx 


d  rhx  +  iji-xn         dtr\ 

"    Tx\_      ~T~     l  =  zArJj   '    '    (I26) 


h-c 


dr                        r_ 
•'•      dt  +  C       ^~=  T (I27) 

First  and  Second  Laws  Combined. — The  combination 
of  equations  (124)  and  (127)  gives 


SATURATED    VAPORS.  1  05 

Natures  of  the  Specific  Heats.  —  Both  the  specific 
pressure  /  and  the  specific  volume  s  of  saturated  vapor 
depend  on  the  temperature,  so  that  we  can  have  neither 
specific  heat  at  constant  volume  nor  specific  heat  at  constant 
pressure,  as  we  had  with  perfect  gases.  The  specific  heat  c 
for  the  liquid  and  the  specific  heat  h  for  the  vapor  are  the 
amounts  of  heat  required  to  raise  the  temperature  of  one  unit 
of  weight  one  degree,  under  the  condition  that  the  pressure 
shall  rise  with  the  temperature,  according  to  the  law  for 
saturated  vapor.  The  volume  of  the  liquid,  indeed,  changes 
so  slowly  that  we  can  ignore  it  ;  but  the  volume  of  the  vapor 
changes  rapidly.  The  specific  heat  of  the  liquid  as  determined 
by  Rowland  up  to  40°  C.  was  at  atmospheric  pressure,  but 
Regnault's  determinations  for  higher  temperatures  were  under 
a  varying  pressure  ;  for  our  present  purpose  we  may  assume 
the  determinations  by  both  experimenters  to  conform  to  our 
definition  just  given. 

Equation  (127)  gives  a  ready  way  of  calculating  the 
specific  heat  for  a  vapor,  for  from  it 

dr        r 


Now  r  may  be  readily  expressed  as  a  function  of  /,  and  then 

dr 
by  differentiation  -j-  may  be  determined.      For  steam 

r  =  X-g  =  606.5  +  0.305*  +  t,  If  c(t  -  *,), 

in  which  f1  is  the  temperature  at  the  beginning  of  the  range, 
as  given  by  the  table  on  page  97,  within  which  t  may  fall. 
Therefore 

dr 

=  0.303  -c, 


and 

- 


h  =  0.305-.       o     .     ,      .     (130) 


106  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

For  other  vapors  the  equations,  deduced  from  the  empirical 
equations  for  A.  and  q  on  pages  98  and  100,  are  somewhat 
more  complicated,  but  they  involve  no  especial  difficulty. 

The  following  table  gives  the  values  of  h  for  steam  at 
several  absolute  pressures: 

SPECIFIC    HEAT    OF   STEAM. 

Pressures,  Ibs.  per  sq.  in., /..        5  50  100  200  300 

Temperatures,  t°  F 162.3         280.9         327.6         381.7         417.4 

Specific  heat,  h —1.607     —1.237     —1.122     — i.ooi     —0.931 

The  negative  sign  shows  that  heat  must  be  abstracted  from 
saturated  steam  when  the  temperature  and  pressure  are 
increased,  otherwise  it  will  become  superheated.  On  the 
other  hand,  steam,  when  it  suddenly  expands  with  a  loss  of 
temperature  and  pressure,  suffers  condensation,  and  the  heat 
thus  liberated  supplies  that  required  by  the  uncondensed 
portion. 

Him  *  verified  this  conclusion  by  suddenly  expanding 
steam  in  a  cylinder  with  glass  sides,  whereupon  the  clear 
saturated  steam  suffered  partial  condensation,  as  indicated  by 
the  formation  of  a  cloud  of  mist.  The  reverse  of  this  experi- 
ment showed  that  steam  does  not  condense  with  sudden  com- 
pression, as  shown  by  Cazin. 

Ether  has  a  positive  value  for  h.  As  the  theory  indicates, 
a  cloud  is  formed  during  sudden  compression,  but  not  during 
sudden  expansion. 

The  table  of  values  of  h  for  steam  shows  a  notable  decrease 
for  higher  temperatures,  which  indicates  a  point  of  inversion 
at  which  h  is  zero  and  above  which  h  is  positive,  but  the 
temperature  of  that  point  cannot  be  determined  from  our 
experimental  knowledge.  For  chloroform  the  point  of  inver- 
sion was  calculated  by  Cazin  f  to  be  123°. 48,  and  determined 
experimentally  by  him  to  be  between  125°  and  129°.  The 
discrepancy  is  mostly  due  to  the  imperfection  of  the  apparatus 

*  Bulletin  de  la  Socie'te'  Industr.  de  Mulhouse^  cxxxiii. 
\  Comptes  rendits  de  I '  Acade'mie  des  Sciences ,  Ixii. 


SATURATED    VAPORS.  107 

used,  which  substituted  finite  changes  of  considerable  magni- 
tude for  the  indefinitely  small  changes  required  by  the  theory. 
Specific  Volume  and  Density.  —  The  most  important 
result  of  the  application  of  the  methods  of  thermodynamics 
to  the  properties  of  saturated  vapor  is  expressed  by  equation 
(128),  which  gives  a  method  of  calculating  the  specific  volume; 
thus: 

dt 

The  numerical  value  of  cr  for  water  for  French  units  is 
o.ooi,  and  for  English  units  is  ^  =  0.016,  nearly.  The 
density,  or  weight  of  a  unit  of  volume,  is  of  course  the 
reciprocal  of  the  specific  volume. 

It  is  of  interest  to  consider  the  degree  of  accuracy  that 
may  be  expected  from  this  method  of  calculating  the  density 
of  saturated  vapor.  The  value  of  r  depends  on  A.  and  q\  for 
the  first  Regnault  gives  three  figures  in  the  data  from  which 
the  empirical  equation  is  deduced,  and  the  experimental  work 
does  not  indicate  a  greater  degree  of  accuracy.  The  fourth 
figure,  if  stated,  is  likely-  to  be  in  error  to  the  extent  of  five 
units.  The  value  of  T  is  commonly  stated  in  four  figures,  of 
which  the  last  may  be  in  error  by  two  units.  A  as  deter- 
mined by  Rowland  has  four  figures,  the  last  being  uncertain 
to  the  extent  of  one  or  two  units.  The  differential  coefficient 

-r  is  deduced  from  the  equations  for  calculating/;  and  those 

equations  are  derived  from  data  having  five  places  of  signifi- 
cant figures.  Now  each  of  the  equations  B  and  C,  for  steam 
at  45°  latitude  for  the  English  system,  gives  a  pressure  of 
14.6967  pounds  on  the  square  inch;  but  the  specific  volume 
calculated  by  aid  of  equation  B  is  26.5,50  cubic  feet,  while 
equation  C  gives  26.637  cubic  feet.^.  The  mean,  26.60,  differs 
from  either  extreme  by.abollt  one  in  seven  hundred.  This 
discrepancy  is  due  to"  ,tnp  fact  that  the  curves  represented  by 


108  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

equations  B  and  C  meet  at  the  common  temperature,  212°, 
but  do  not  have  a  common  tangent.  Since  the  equations  are 
empirical  and  not  logical,  the  error  or  uncertainty  is  unavoid- 
able, and  all  calculated  specific  volumes  are  affected  by  a 
similar  uncertainty.  The  greatest  probable  error  is  in  deter- 
mining r,  for  which  it  may  be  about  one  in  one  thousand. 
The  error  introduced  into  this  equation  by  using  the  values  of 
A  in  common  use,  that  is,  772  instead  of  778,  is  about  one  in 
one  hundred. 

In  all  recent  tables  of  the  properties  of  saturated  vapor 
the  specific  volumes  are  calculated  by  the  method  just  dis- 
cussed, on  account  of  the  great  difficulty  of  experimental 
determinations.  The  error  of  the  calculation  is  not  greater 
than  the  errors  of  some  other  parts  of  the  table  which  are 
determined  by  direct  experiments. 

Experimental  Determinations  of  Specific  Volume. — 
The  uncertainty  of  the  direct  determination  of  the  density 
of  saturated  vapor  is  due  to  the  difficulty  of  determining  when 
it  is  dry  and  saturated ;  a  small  quantity  of  liquid  present  or 
a  slight  degree  of  superheating  will  introduce  serious  errors. 

Two  series  of  tests  of  the  specific  volume  of  saturated 
vapors  have  been  made,  by  Tate  and  Fairbairn  *  and  by 
Perot. f  Though  made  with  much  skill  and  ingenuity,  the 
experiments  by  Tate  and  Fairbairn  are  affected  by  so  large 
experimental  errors  that  they  would  have  very  little  interest 
were  it  not  that  some  tables  of  the  properties  of  saturated 
steam  now  in  use  depend  partly  on  these  tests.  The  highest 
pressure  used  for  these  tests  was  1 14  inches  of  mercury,  or 
about  50  pounds  absolute  per  square  inch.  Within  this 
range  the  error  of  Tate  and  Fairbairn's  empirical  equation 
deduced  from  their  experiments  is  three  or  four  per  cent; 
beyond  fifty  pounds  the  errors  become  very  large.  The 
empirical  equation  just  referred  to  is 


*  Philosophical  Transactions ',  vol.  cl,  1860. 

f  Journal  franklin  Institute,  vol.  cxxxiii,  p.  55. 


SATURATED    VAPORS. 


109 


=  25.62  + 


49513 

P+0.72' 


where  Fis  the  volume  of  steam  compared  with  that  of  the 
water  from  which  it  is  produced,  and  P  is  the  pressure  in 
inches  of  mercury. 

The  principal  difficulty  in  making  direct  determinations  of 
specific  volumes  of  saturated  vapor  is  to  be  sure  that  the 
vapor  is  neither  moist  nor  superheated.  For  this  purpose 
Perot  enclosed  a  glass  globe  for  weighing  the  vapor  in  a 
strong  receptacle  together  with  a  sealed  tube  of  the  liquid  to 
be  tested.  Both  the  receptacle  and  the  globe  were  exhausted 
by  an  air-pump,  then  the  temperature  was  raised  and  the  tube 
of  liquid  was  broken,  and  the  receptacle  and  the  ^lobe  were 
filled  with  vapor.  The  globe  was  supported  on  a  frame,  so 
as  not  to  be  directly  in  contact  with  the  walls  of  the  recepta- 

PEROT'S    EXPERIMENTS    ON    SPECIFIC    VOLUMES   OF 
SATURATED    VAPOR. 


Name  of  Vapor. 

Temperatures. 

Specific  Volumes,  Cubic  Metres. 

Experimental. 

By  Equation  (131). 

Difference. 

68.20 
88.60 
98.10 
99.60 
IOI.5O 
124.10 

5-747 
2-531 
'1.782 

1.657 
1-583 
0.766 

5-428 
2.469 
1.768 
1.683 
1.583 
0.7804 

0-329 
0.062 
0.014 
—  0.026 
o.o 
—  0.14 

Bisulphide  of 

84.60 

0.1163 

O.I2I 

—  0.005 

Ether    

28.40 
30.00 
31.70 
31.90 
57-90 
85.50 
IIO.5O 

0.4262 
0.4000 
o.375i 
0.3730 
0.1680 
0.07777 
0.04394 

0.429 
0.4013 
0.382 
0.380 

o.  169 

0.082 
0.0454 

—  0.003 
—  0.0013 
—  0.007 
—  0.007 

—  O.OOI 

—  0.004 
—  0.0015 

cle,  and  being  filled  with  vapor  and  surrounded  by  vapor  at 
the  same  pressure  it  is  fair  to  conclude  that  it  was  at  the 


110  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

temperature  due  to  the  pressure  of  the  vapor  and  that  it  con- 
tained only  dry  saturated  vapor.  In  preparation  for  the 
experiment  the  mouth  of  the  globe  was  drawn  down  to  a  fine 
tube,  around  which  a  platinum  wire  was  wound,  so  that  at  the 
proper  time  the  opening  could  be  closed  by  passing  an  electric 
current  through  the  wire.  After  the  globe  was  sealed  full  of 
dry  saturated  vapor  the  receptacle  was  opened  and  the  globe 
taken  out  and  weighed. 

The  results  of  these  tests  are  shown  in  the  accompanying 
table,  together  with  values  calculated  by  aid  of  equation  (131). 

Zeuner's  Equation  for  Internal  Heat. — The  following 
•empirical  equations  were  proposed  by  Zeuner  for  calculating 
the  heat  equivalent  of  the  disgregation  work  during  vaporiza- 
tion. They  are  most  interesting  from  the  light  they  throw 
on  the  critical  temperature. 


INTERNAL   LATENT    HEAT. 

French  Units. 

Water p  —  575-4Q  —  0.791* 

Ether p=    86.54  —  0.10648^  —  o.oooyiGo/2 

Chloroform p  =    62.44  —  0.11282^  —  o.ooooi4o/9 

Carbon  bisulphide p  —     82.79  —  0.11446^  —  0.0004020^* 

Carbon  tetrachloride p  —    48.57  —  0.06844^  —  o.ooo2o8o/8 

Aceton p  =  131.63  —  0.20184^  —  o.ooo628o/2 

The  following  table  shows  that  the  equation  for  water 
gives  a  fair  degree  of  approximation : 

0°  50°  100°  150°  200° 

By  equation  (117) 575.5     536.3     496.4    457.4    417.4 

By  empirical  equation. ..    575.4     535.9    496.3    456.8    417.1 

Critical  Temperature.  —  The  empirical  equation  for 
steam,  and  also  the  value  of  p  in  the  table  above  by  the  exact 
method,  show  that  the  internal  latent  heat  decreases  as  the 
temperature  rises,  and  at  sufficiently  high  temperatures  it  will 
approach  zero.  If  p  is  made  zero  in  Zeuner's  equation  for 


SATURATED    VAPORS.  Ill 

steam  the  corresponding  temperature  is  720°  C.,  which  indi- 
cates that  the  true  point  is  much  beyond  the  limits  of  experi- 
ments. 

The  temperature  at  which  p  becomes  zero  for  any  vapor 
is  called  the  critical  temperature,  for  at  that  temperature  the 
distinction  between  the  liquid  and  its  vapor  vanishes,  and 
above  that  temperature  the  vapor  or  gas  cannot  be  liquefied 
by  pressure  alone.  It  has  been  proposed  to  call  a  substance 
which  is  above  the  critical  temperature  a  gas,  and  one  which 
is  below  a  vapor. 

Experiments  on  liquids  strongly  heated  in  strong  glass 
tubes  show  that  vaporization  proceeds  gradually  as  the  tem- 
perature rises,  until  a  temperature  is  reached  at  which  the  line 
of  demarcation  between  the  liquid  and  its  vapor  becomes 
indistinct.  Above  that  temperature  the  liquid  all  disappears, 
and  the  tube  is  full  of  gas.  This  is  the  critical  temperature. 
Avenarius  *  by  this  method  determined  the  critical  tempera- 
ture of  four  liquids.  He  also  selected  from  Regnault's 
experiments  the  data  most  applicable,  and  from  them  deduced 
-equations  like  those  given  by  Zeuner  for  the  internal  latent 
heat  of  vapors,  and  calculated  the  critical  temperature  by 
their  aid.  The  results  are  as  follows: 

Experimental.          Calculated. 

Ether.... 196°. 2  C.  196°. 8  C. 

Carbon  bisulphide 276°.  I  274°. o 

Carbon  tetrachloride   292°. 5  298°. 7 

Aceton 246°.  i  2 30°. 4 

Curve  of  Constant  Steam  Weight. — It  was  formerly 
-assumed  in  the  theory  of  the  steam-engine  that  the  inter- 
change of  heat  between  the  steam  and  the  iron  of  the  cylinder 
was  by  radiation;  and,  further,  that  the  condensation  accom- 
panying adiabatic  expansion  formed  a  cloud  which  instigated 
a  rapid  interchange  of  heat  where  before  little  had  occurred. 
The  steam-jacket  was  assumed  to  impart  just  heat  enough  to 

*  Poggendorff  s  Annalen,  cli,  1874. 


112  THERMODYNAMICS    OF    THE   STEAM-EA7G7NE. 

dissipate  this  cloud  and  keep  the  steam  dry.  Hence  the 
curve  of  dry  saturated  steam  was  considered  to  be  of  great 
importance  in  the  theory  of  the  steam-engine,  and  it  is  some- 
times drawn  on  indicator-cards  instead  of  the  hyperbola. 
The  substitution  has  no  good  reason,  for  the  curve  is  not  a 
better  approximation  to  the  curve  drawn  by  an  indicator,  and 
is  more  troublesome  to  construct. 

The  action  of  steam  in  the  engine-cylinder  has  been 
proved  to  be  quite  different,  for  an  interchange  of  heat  is 
caused  by  condensation  by  contact  of  the  steam  with  the  iron, 
or  by  evaporation  of  moisture  from  it,  and  the  curve  of 
saturated  steam  no  longer  plays  an  important  part  in  the 
theory  of  the  steam-engine.  Still  it  is  of  importance  as  form- 
ing the  boundary-line  between  superheated  steam  and  wet 
steam. 

The  curve  may  be  represented  very  closely  by  the  ex- 
ponential formula 

pvn  —  p^v"  —  const (J32) 

Rankine  proposed  the  value  -f-J  for  the  exponent  n,  and 
Zeuner  has  found  that  1.0646  gives  still  a  closer  approxima- 
tion.    The  actual  curve  may  be  drawn  by  plotting  pressures- 
and  volumes  from  a  table  of  the  properties  of  saturated  steam. 

Isothermal  Lines. — Since  the  pressure  of  saturated  vapor 
is  a  function  of  the  temperature  only,  the  isothermal  line  of  a 
mixture  of  a  liquid  and  its  vapor  is  a  line  of  equal  pressures, 
parallel  to  the  axis  of  volumes.  Steam  expanding  from  the 
boiler  into  the  cylinder  of  an  engine  follows  such  a  line;  that 
is,  the  steam-line  of  an  automatic  cut-off  engine  with  ample 
ports  is  nearly  parallel  to  the  atmospheric  line. 

The  heat  required  for  an  increase  of  volume  at  constant 
pressure  is 

Q  =  r(x,  -  *,), 

which  may  be  obtained  by  integrating  equation  (119)  with  the 
assumption  that  the  temperature  is  constant;  or  it  may  be 


SATURATED    VAPORS.  113 

written   directly,    since   r  is   the    heat  of    vaporization,    and 
x^  —  xl  is  the  weight  of  liquid  vaporized. 

The  work  done  by  the  vapor  during  such  an  expansion  is 

^  =  X*.-*0  =/*(*.-*,)•    •      •     •     033) 

Isodynamic  or  Isoenergic  Lines.  —  The  following  method 
of  treating  the  isodynamic  changes  of  a  mixture  of  a  liquid 
and  its  vapor  gives  the  solution  of  all  problems  that  arise, 
although  it  does  not  give  an  equation  to  the  curve  of 
pressures  and  volumes. 

The  increase  of  intrinsic  energy  of  the  mixture  of  a  liquid 
and  its  vapor,  above  freezing-point,  is 


(134) 


where  q  and  xp  are  the  heat-equivalents  of  the  vibration  and 
disgregation  works.  The  change  of  intrinsic  energy  in  passing 
from  one  condition  to  another  is 


When  the  change  is  isodynamic,  the  energy  remains  the 
same  by  definition,  and 


,  —  *XA  =  o;      .     .      .     (136) 
which  equation,  together  with  the  formulae 

*.  =  *,«.+  °".      v*  =  *&  +  *,.     •      •     (137) 

gives  the  means  of  solving  all  problems. 

For  example,  if  a  mixture  of  T97  steam  and  ^  water 
expands  isoenergically  from  100  pounds  absolute  to  15  pounds 
absolute  the  final  condition  will  be 

?i  —  £.  +  *iPi       297.9—  181.8  +  0.9X802.8 

*'=       ~7,~  892.6  -  =  0.9395. 


•     f~ 


114  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  initial  and  final  specific  volumes  are 

^  =  xlul  +  o-  =  0.9(4,403  —  0.0160)  +  0.0160  =  3.964; 
z'a  =  xji^  +  o-  =  0.9395(26.15  —  0.016)  +  0.016  =  24.54. 

The  converse  problem  requiring  the  pressure  corresponding 
to  a  given  volume  cannot  be  solved  directly.  The  only 
method  of  solving  such  a  problem  is  to  assume  a  probable  final 
pressure  and  find  the  corresponding  volume ;  then,  if  necessary, 
assume  a  new  final  pressure  larger  or  smaller  as  may  be 
required,  and  solve  for  the  volume  again ;  and  so  on  until  the 
desired  degree  of  accuracy  is  obtained. 

\\  The  isoenergic  line  can  be  well  represented  by  an  expo- 
nential equation,  for  which  the  exponent  can  be  determined 
by  the  method  given  on  page  69.  This  is  very  fortunate,  as 
there  is  no  ready  way  of  calculating  the  external  work  by  the 
aid  of  the  usual  tables  of  the  properties  of  saturated  steam. 
Having  given  or  determined  the  initial  and  final  volumes, 
the  exponential  equation  may  be  determined,  and  then  the 
external  work  may  be  calculated  by  the  equation 


w  = 


For  example,  the  exponent  for  the  equation  representing 
the  expansion  of  the  problem  on  page  113  is 

i,"«iv 

n  _±  log  A  -  log  A  =      log  IPO-  log  15       _  i 
log  vt  —  log  v,       log  24.54  —  log  3.964 


and  the  external  work  of  expansion  is 


zoo  X  144  X  3.964  j 

1.041  -  i  [  24.  54/ 


w=  r  _  I0000oft..lbs. 


Since  there  is  no  change  in  the  intrinsic  energy  during  an 
isoenergic  expansion,  the  external  work  is  equivalent  to  the 


SATURATED    VAPORS.  11$ 

heat  applied.     Thus   in   the   example   just  solved   the    heat 
applied  is  equal  to 

100000  -r-  778  =  129  B.  T.  u. 

Entropy  of  the  Liquid.  —  Suppose  that  a  unit  of  weight 
of  a  liquid  is  intimately  mingled  with  its  vapor,  so  that  its 
temperature  is  always  the  same  as  that  of  the  vapor;  then  if 
the  pressure  of  the  vapor  is  increased  the  liquid  will  be 
heated,  and  if  the  vapor  expands  the  liquid  will  be  cooled. 
So  far  as  the  unit  of  weight  of  the  liquid  under  consideration 
is  concerned  the  processes  are  reversible,  for  it  will  always  be 
at  the  temperature  of  the  substance  from  which  it  receives  or 
to  which  it  imparts  heat,  i.e.,  it  is  always  at  the  temperature 
of  its  vapor. 

The  change  of  entropy  of  the  liquid  can  therefore  be  cal- 
culated by  equation  (36), 


d<f>  =  —., 


which  may  here  be  written 


Now  the  specific  heat  of  water  as  given  in  the  table  on 
page  97  is  constant  within  certain  ranges  and  varies  from  one 
range  to  the  next  range  of  temperature.  The  calculation,  like 
that  for  the  heat  of  the  liquid,  must  be  made  step  by  step. 

For  example^  the  increase  of  entropy  of  water  from  freez- 
ing-point to  13°  C.  is 

T  T  T 

1.0072    log,  -^r  +   1.0044  log,  -^  +   I.OOI6  loge  -^  =  0.04663. 


For  a  liquid  like  ether  which  has  the  heat  of  the  liquid 
represented  by  an  empirical  equation, 

q  =  0.52901*  +  0.0002959/*, 


Il6  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

the  specific  heat  is  first  obtained  by  differentiation,  giving 
c  =  0.52901  +  o.ooo59i8/. 

Then  the  increase  of  entropy  above  that  for  the  freezing-point 
of  water  maybe  obtained  by  aid  of  equation  (139);  which 
gives  for  ether  with  the  French  system  of  units 

6=   f    j  0.52901  +o.ooo59i8(r-  273.7)!  -=; 
^273.7  (  )  2 

rTf          dt  \ 

.-.  0  =    I      0.3670^  +  0.0005918^  ; 
</273.7V  1  I 

T 
.-.  6  =  O.ooo59i8(r-  273.7)  +  0.3670  lo 


T 
.-.  6  =  0.0005918^  +  0.3670  log,       -.       .     .     .     (140) 


For  temperatures  below  the  freezing-point  of  water  equa- 
tion (140)  gives  negative  numerical  results. 

Other  liquids  for  which  equations  for  the  heat  of  the  liquid 
are  given  on  page  98,  may  be  treated  in  a  similar  method. 

Tables  of  the  properties  of  saturated  vapor  should  include 
entropies  of  the  liquid,  calculated  from  freezing-point,  by  one 
of  the  methods  just  illustrated.  If  such  tables  are  not  at  hand, 
then  changes  in  the  entropy  of  the  liquid  may  be  calculated 
approximately,  on  the  assumption  that  the  specific  heat  is  a 
constant  by  the  equation 


Entropy  due  to  Vaporization.  —  When  a  unit  of  weight 
of  a  liquid  is  vaporized  r  thermal  units,  equal  to  the  heat  of 
vaporization,  must  be  applied  at  constant  temperature.  If 
only  the  portion  x  is  vaporized,  then  xr  thermal  units  are 
applied.  Treating  such  a  vaporization  as  a  reversible  process, 
the  change  of  entropy  may  be  calculated  by  the  equation 


0-  0,  =  =dQ=~.      .     .     (142) 


SATURATED    VAPORS.  II  7 

Entropy  of  a  Mixture  of  a  Liquid  and  its  Vapor.  —  The 

increase  in  entropy  due  to  heating  a  unit  of  weight  of  a  liquid 
from  freezing-point  to  the  temperature  t  and  then  vaporizing 
x  portion  of  it  is 


where  6  is  the  entropy  of  the  liquid  and  r  is  the  heat  of 
vaporization,  both  of  which  are  given  in  tables  of  the  proper- 
ties of  vapors;  while  T  is  obtained  by  adding  the  absolute 
temperature  of  zero  to  the  temperature  by  the  thermometer. 
For  any  other  state  determined  by  xl  and  /,  we  shall  have, 
for  the  increase  of  entropy  above  that  of  liquid  at  freezing- 
point, 


The  change  of  entropy  in  passing  from  one  state  to 
another  is 

0  -    0,  =   Y  +  0  -  ~   -   Bl  .    .        .        .        (I44) 

When  the  condition  of  the  mixture  of  a  liquid  and  its 
vapor  are  given  by  the  pressure  and  value  of  x,  then  a  table 
giving  the  properties  at  even  pressures  may  be  conveniently 
used  for  this  work. 

Adiabatic  Equation  for  a  Liquid  and  its  Vapor.  —  Dur- 
ing an  adiabatic  change  the  entropy  is  constant,  so  that  equa- 
tion (144)  gives 


When  the  initial  state,  determined  by  x^  and  /,  or  pl9  is 
known  and  the  final  temperature  /3,  or  the  final  pressure  /„ 
the  final  value  x^  may  be  found  by  equation  (145).  The 
initial  and  final  volumes  may  be  calculated  by  the  equations 

vl  =  ^iul  -)-  cr     and     ^a  =  xjit  +  <r.   .     .     (146) 


Il8  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Tables  of  the  properties  of  saturated  vapors  commonly 
give  the  specific  volume  j,  but 

s  =  u  -f-  a. 

Values  of  cr  will  be  found  on  page  101. 

Problems  in  which  the  initial  condition  and  the  final  tem- 
perature or  pressure  are  given  may  be  solved  directly  by  aid 
of  the  preceding  equations.  Those  giving  the  final  volume 
instead  of  the  temperature  or  pressure  can  be  solved  only  by 
approximations.  An  equation  to  an  adiabatic  curve  in  terms 
of/  and  v  cannot  be  given,  but  such  a  curve  for  any  particular 
case  may  be  constructed  point  by  point. 

Clausius  and  Rankine  independently  and  at  about  the 
same  time  deduced  equations  identical  with  equations  (144) 
and  (145),  but  by  methods  each  of  which  differed  from  that 
given  here. 

In  the  discussion  of  the  specific  heat  h  of  a  saturated 
vapor,  it  appeared  that  the  expansion  of  dry  saturated  steam 
in  a  non-conducting  cylinder  would  be  accompanied  by  partial 
condensation.  The  same  fact  may  be  brought  out  more 
clearly  at  this  place. 

For  example,  one  pound  of  dry  steam  at  100  pounds  abso- 
lute pressure  will  have  the  values 

/t  =  327°-58  F.,     r,  =  884.0,      ^=0.4733, 
If  the  final  pressure  is  15  pounds  absolute,  we  have 
03  F.,     rt  =  965.1,      0,  =  0.3143; 


whence 

884.0   ,  965.1*, 


.'.    *,   =   0.8948. 

On  the  other  hand,  h  is  positive  for  ether,  and  partial 
condensation  takes  place  during  compression  in  a  non-con- 
ducting cylinder. 


SA  TURA  TED     VA  /  ORS.  1 1 9 

For  example,  let  the  initial  condition  be 

/,  =  10°  C.,        r,  =  93.12,      #,=0.0191,     -*,=  !, 
and  let  the  final  conditions  be 

/,  =  120°  C.,      ra  =  72.26,      0a  =  0.2045  ; 


then 


03.12  72.26^, 

+  0.0191  =  '—       -'  +  0.2045, 


283-7  393-7 

and 

*,  =  0.724. 

Equation  (145)  applies  to  all  possible  mixtures  of  a  liquid 
and  its  vapor,  including  the  case  of  xl  =  o  or  the  case  of  liquid 
without  vapor,  but  at  the  pressure  corresponding  to  the  tem- 
perature according  to  the  law  of  saturated  vapor.  When 
applied  to-hot  water,  this  equation  shows  that  an  expansion 
in  a  non-conducting  cylinder  is  accompanied  by  a  partial 
vaporization. 

There  is  some  initial  state  of  the  mixture  such  that  the 
value  of  x  shall  be  the  same  at  the  beginning  and  at  the  end, 
though  it  may  vary  at  intermediate  states.  To  find  that  value 
make  x^  =  x^  in  equation  (145)  and  solve  for  xl9  which  gives 


rt     7; 

The  value  of  x^  for  steam  to  fulfil  the  conditions  given  varies 
with  the  initial  and  final  temperatures  chosen,  but  in  any  case  it 
will  not  be  much  different  from  one  half.  It  may  therefore 
be  generally  stated  that  a  mixture  of  steam  and  water,  when 
expanded  in  a  non-conducting  cylinder,  will  show  partial  con- 
densation if  more  than  half  is  steam,  and  partial  evaporation 
if  more  than  half  water.  If  the  mixture  is  nearly  half  water 
and  half  steam,  the  change  must  be  investigated  to  determine 
whether  evaporation  or  condensation  will  occur;  but  in  any 
case  the  action  will  be  small. 


120  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

External  Work  during  Adiabatic  Expansion. — Since 
no  heat  is  transmitted  during  an  adiabatic  expansion,  all  of 
the  intrinsic  energy  lost  is  changed  into  external  work,  so 
that,  by  equation  (134), 

W=  E,-  E,  =  -j(&  -  q,  +  x,Pl  -  x,p,}.    .      (148) 

For  example,  the  external  work  of  one  pound  of  dry  steam 
in  expanding  adiabatically  from  100  pounds  to  15  pounds 
absolute  is 

W=  778(297.9  —  181.8  +  I  X  802.8  —  0.8948  X  892.6) 
—  935 x  5  foot-pounds. 

The  adiabatic  curve  cannot  be  well  represented  by  an 
exponential  equation;  for  if  an  exponent  be  determined  for 
such  a  curve  passing  through  points  representing  the  initial 
and  final  states,  it  will  be  found  that  the  exponent  will  vary 
widely  with  different  ranges  of  pressure,  and  still  more  with 
different  initial  values  of  x;  and  that,  further,  the  inter- 
mediate points  will  not  be  well  represented  by  such  an 
exponential  curve  even  though  it  passes  through  the  initial 
and  final  points. 

This  fact  was  first  pointed  out  by  Zeuner,  who  found  that 
the  most  important  element  in  determining  n  was  x^  the 
initial  condition  of  the  mixture.  He  gives  the  following 
empirical  formula  for  determining  n,  which  gives  a  fair 
approximation  for  ordinary  ranges  of  temperature: 

*=  1.035 +0.100*,.     •      •      .      .     (149) 

There  does  not  appear  to  be  any  good  reason  for  using  an 
exponential  equation  in  this  connection,  for  all  problems  can 
be  solved  accurately  by  the  method  given,  and  the  action  of 
a  lagged  steam-engine  cylinder  is  far  from  being  adiabatic. 
An  adiabatic  line  drawn  on  an  indicator-diagram  is  instructive, 
since  it  shows  to  the  eye  the  difference  between  the  expan- 
sion in  an  actual  engine  and  that  of  an  ideal  non-conducting 


tfl 


SATURATED    VAPORS.  121 

cylinder;  but  it  can  be  intelligently  drawn  only  after  an 
elaborate  engine  test.  For  general  purposes  the  hyperbola  is 
the  best  curve  for  comparison  with  the  expansion  curve  of  an 
indicator-diagram,  for  the  reason  that  it  is  the  conventional 
curve,  and  is  near  enough  to  the  curve  of  the  diagrams  from 
good  engines  to  allow  a  practical  engineer  to  guess  at  the 
probable  behavior  of  an  engine,  from  the  diagram  alone.  It 
cannot  in  any  sense  be  considered  as  the  theoretical  curve. 

EXAMPLES. 

1.  Calculate  the  pressure,  heat  of  the  liquid,  total  heat, 
heat  of  vaporization,  specific  volume,  etc.,  at  several  tempera- 
tures for  the  vapors  for  which   the  data  and   equations  are 
given,  and  compare  with  results  given  in  the  Tables  of  the 
Properties  of  Saturated  Steam. 

2.  Find  the  external  work  of  expansion  of  a  fluid,  follow- 
ing the  law  given  by  the  equation  pv*,  which  has  the  initial 
volume    3    cubic   metres   and    the   initial   pressure  4   atmos- 
pheres,  and  which   expands   till   the   pressure   becomes  one 
atmosphere.  Ans.  133660  kgm. 

3.  A  pound  of  steam  and  water  at  150  pounds  pressure  is 
O.6  steam;  what  is  the  increase  of  entropy  above  that  of  water 
at  32°  F.  ?  Ans.  1.1442. 

4.  A  kilogram  of  chloroform  at  100°  C.  is  0.8  vapor;  what 
is  the  increase  of  entropy  above  that  of  the  liquid  at  o°  C.  ? 

Ans.  o.  1959. 

5.  The  initial  condition  of  a  mixture  of  water  and  steam 
is  t  =  320°  F.,   ;tr  =  o.8;    what    is  the  final    condition  after 
adiabatic  expansion  to  212°  F.  ?  Ans.  0.7398. 

6.  The  initial  condition  of  a  mixture  of  steam  and  water 
is/  =  3000  mm.,  x  =  0.9;   find  the  condition  after  an  adia- 
batic expansion  to  600  mm.  Ans.  0.8278. 

7.  A  cubic  foot  of  a  mixture  of  water  and  steam,  x  =  0.8, 
is  under  the  pressure  of  60  pounds  by  the  gauge.      Find  its 
volume    after  it    expands    adiabatically  till   the    pressure   is 


122  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

reduced  to  10  pounds  by  the  gauge;   also  the  external  work 
of  expansion.  Ans.  2.6857  cu-  ft-  an<^  99^ l  ft.-lbs. 

8.  Three  pounds  of  a  mixture  of  steam  and  water  at  120 
Ibs.   absolute  pressure  occupy  4.5   cu.   ft.      How  much  heat 
must  be  added  to  double  the  volume  at  the  same  pressure 
and  what  is  the  change  of  intrinsic  energy  ? 

Ans.  1065  B.T.U.;   750400  ft.-lbs. 

9.  A  test  of  an  engine  with  the  cut-off  at  o.  106  of  the 
stroke,  and  the  release  at  0.98  of  the  stroke,  and  with  4.5  per 
cent  clearance,  gave  for  the  pressure  at  cut-off  62.2   pounds 
by  the  indicator,  and  at  release  6.2  pounds;   the  mixture  in 
the  cylinder  at  cut-off  was  0.465   steam,  and  at  release  0.921 
steam.      Find  (i)  condition   of  the  mixture  in  the  cylinder  at 
release  on   the  assumption  of  adiabatic  expansion  to  release; 
(2)   condition   of   mixture   on  the  assumption   of   hyperbolic 
expansion,  or  that  pv  =  plvl ;  (3)  the  exponent  of  an  exponen- 
tial curve  passing  through  points  of  cut-off  and  release;   (4) 
exponent   of   a   curve  passing  through   the    initial   and    final 
points   on    the   assumption   of   adiabatic   expansion;    (5)   the 
piston  displacement  was  0.7  cubic  feet,  find  the  external  work 
under  exponential  curve  passing  through  the  points  of  cut-off 
and  release;  also  under  the  adiabatic  curve. 

Ans.  (1)0.472;  (2)0.524;  (3)»  =  0.6802;  (4)  n  =  1.0589; 
(5)  3°93  and  2120  ft.-lbs. 


CHAPTER  VII. 
SUPERHEATED   VAPORS. 

A  DRY  and  saturated  vapor,  not  in  contact  with  the  liquid 
from  which  it  is  formed,  may  be  heated  to  a  temperature 
greater  than  that  corresponding  to  the  given  pressure  for  the 
same  vapor  when  saturated  ;  such  a  vapor  is  said  to  be  super- 
heated. When  far  removed  from  the  temperature  of  satura- 
tion such  a  vapor  follows  the  laws  of  perfect  gases  very 
nearly,  but  near  the  temperature  of  saturation  the  departure 
from  those  laws  is  too  great  to  allo^of  calculations  by  them 
for  engineering  purposes. 

In  the  case  of  superheated  steam  various  provisional 
characteristic  equations  have  been  proposed  for  use  until  the 
necessary  experimental  investigation  shall  give  the  data  for  a 
true  theory.  The  theory  given'here  was  proposed  by  Zeuner. 
It  is  convenient  for  calculation  and  appears  to  give  good 
results.  * 

Substituting  in  the  characteristic  equation  for  a  gas 

pv=RT, 
the  value  of  R  from  equation  (64)  gives  ^ 


f  he  form  of  characteristic  equation  proposed  by  Zeuner 
for  superheated  steam  is 

tv  =  -%   k-=^-  T-Cf.      .    ,    -     .    (ISO 

133 


124  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  specific  heat  at  constant  pressure  cp  is  assumed  to  be 
constant,  k  is  a  constant  suggested  by  the  ratio  K  of  the 
specific  heats  of  a  gas;  but  it  will  be  shown  that  the  specific 
heat  at  constant  volume,  determined  from  the  equation  (151), 
is  a  variable;  consequently  k  cannot  be  the  ratio  of  the  specific 
heats  of  superheated  steam.  C  and  a  are  constants  that  are 
to  be  determined  from  the  known  properties  of  saturated  and 
superheated  steam. 

Partial  Differential  Coefficients.  —  From  the  character- 
istic equation  (151)  maybe  deduced  the  partial  differential 
coefficients 

Apk 


dt\  Avk  apa 

~-~ 


Application  of  the  First  Law.  —  The  first  law  of  ther- 
modynamics may  be  conveniently  applied  by  using  equation 
(48),  substituting  for  n  and  o  their  values,  in  terms  of  the 
specific  heats,  from  the  proper  equations  on  page  13;  thus: 


_1  I  (<*!L\      (d!^\  \ 
A  \  \d!v     \fa)  J  ~~ 


dt  idt 

=  ' 


.  _A     (IS4) 

-"•   •    •    U54) 


In  applying  this  equation  it  is  convenient  to  substitute  for 
J    from  equation  (152),  perform  the  d 
cated,  and  then  simplify  the  result,  giving 


i-j-J    from  equation  (152),  perform  the  differentiation  indi- 


SUPERHEATED    VAPORS.  12$ 


(ISS) 


(ISO 

=!=!•  •  •  (I56) 

If  this  expression  is  integrated  we  get  a  new  expression 
for  the  partial  differential  coefficient  U=J  instead  of  the 
somewhat  complicated  expression  of  equation  (152),  namely, 
dt\  Av 


Application  of  the  Second  Law.  —  Equation  (55), 


deduced  by  the  successive  application  of  the  two  laws  of 
thermodynamics,  can  be  most  conveniently  used  in  this  place. 
Substituting  the  values  of  the  partial  differential  coefficients 
from  equations  (152)  and  (157)  gives 

(*  -  i)'    T 


which  gives  the  method    of  calculating  the  specific  heat  at 
constant  volume  when  ct  and  k  are  known. 

Exponent   a.  —  Equating  the  values    of   the    differential 
coefficient  given  by  equations  (152)  and  (157),  we  have 

Av  Avk          apa-^AkC 

H~ 


C,(k-    I)          Cf(k-    I)     '     Cf(k-    I)' 


126  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Simplifying  and  solving  for  a,  we  have 


~ 


Substituting  the  values  of  —  and  of  Cpa  from  equations  (158) 

^v 

and  (151), 


-1 


_ 
a~~ 


pv  p        k       Apv 

~k~  k-  i  T 

PV-C*-TA 


(159) 


Characteristic  Equation  for  Superheated  VaporX-Sub- 

stituting  the  value  deduced  for  a  in   equation  (i5i)"gives,  for 
the  characteristic  equation  for  superheated  steam, 


k 


(160) 


Thermal  Capacities.  —  From  equations  (n),   (152),   and 
(158), 

*-''     T 


(161) 


From  equations  (15),  (157),  and  (158), 

k~l*  T     Av 


p  c      -  i 

k-iT 


'>—  Tp 


SUPhRHEATMD    VAPORS.  12; 

From  equations  (17)  and  (152), 


From  equations  (18)  and  (157), 


QAv 
r=J^r 


General  Equations.—  Substituting  the  values  of  /,  m,  nt 
,and  o  in  equations  (5),  (6),  and  (7)  gives,  for  the  general  equa- 
tions for  superheated  steam, 


-i)dv      •    .     .     (165) 


It  is  instructive  to  compare  these  equations  with  the 
general  equations  (70),  (71),  and  (72)  for  perfect  gases,  which 
may  be  written, 


<IQ= 


v\  .....     (170) 

K.     •••• 


128  THERMODYNAMICS   OF    THE   STEAM-ENGINE. 

To  obtain  equation  (170),  equation  (72)  may  be  written, 

dQ  —  cv-gdp  -f  cp-gdv  ; 

Acvv  Acpp 

•"'    dQ  =  T~dp+  7~cdv' 

CP   —    Cv  cp   —   Cv 

It  is  to  be  remarked  that  equation  (165)  is  not  useful  in 
its  present  form,  since  cv  is  a  variable,  but  it  is  written  for 
symmetry  in  comparison  with  equations  (168),  (169),  and 
(170). 

Entropy.  —  Equation  (166)  gives 

dQ  (  dt       k-idp 

-  -r-j 

T      k  —  i 


0-  0,  =  , 


which  is  to  be  compared  with  equation  (89),  page  71,  for  gases. 
Equations  (165)  and  (167)  cannot  conveniently  be  used  for 
calculating  change  of  entropy. 

Value  of  k.  —  The  characteristic  equation  for  superheated 
vapor  is  intended  to  apply  to  all  degrees  of  superheating, 
approaching  at  one  limit  the  condition  of  a  gas,  and  at  the 
other  that  of  saturated  vapor.  For  a  mixture  of  a  liquid  and 
its  vapor  we  have,  from  equation  (144), 


or  for  saturated  steam  with  x  =  i 

~(cdt  +  dr-^dt]..     (173) 


SUPERHEATED    VAPORS.  129 

Equations  (171)  and  (173)  should  both   be   true  for  dry 
saturated  vapor,  whence 


k-\Tdp\  dr 


By  equation  (129)  the  right-hand  member  of  equation 
(174)  is  equal  to  hy  the  specific  heat  of  saturated  vapor;  con- 
sequently 

k  —  i        cp  —  h 

—  =  T         ....... 


f  dtc* 


Superheated  Steam.  —  Regnault  gives  as  the  results  of 
three  experiments  on  the  specific  heat  of  superheated  steam 
at  constant  pressure 

0.48111,          0.48080,          0.47963, 

and  for  the  mean  value 

cp  =  0.4805. 

With  this  value  of  cp  and  the  known  values  of  the  other 
factors,  determined  from  the  properties  of  saturated  steam, 
the  following  values  of  k  were  calculated  : 

Pressure,  pounds  ) 

5  50  100          200         300 

on  the  sq.  in.     ) 

k  1.33         1-332       1.330       1.324 

Zeuner  assumed  for  the  constant  k  the  value 
k=  $  =  I.333+. 


130  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

which  may  be  compared  with  the  ratio  of  the  specific  heats  of 
air,  3  - 

K  —    1.405. 

With  this  assumed  value  of  k  and  the  known  values  of  A 
and  cp  the  coefficient  of  T  in  the  characteristic  equation  (160) 
becomes: 

French  system,       -|-    ~T—  =  B  =  51.28; 

c    fc j 

English  system,      -4  — -r—  =  B  =  93.46. 


The  specific  volume  of  saturated  steam  under  atmospheric 
pressure  and  at  boiling-point  is  26.60  cubic  feet  or  1.661 
cubic  metres.  Solving  equation  (160)  for  C, 

C      k  —  l 


and  therefore  we  have: 

French  system, 

51.28  X  373-7-  IQ333  X   1.661 

L  =  -  "i =  190.4; 

10333* 

English  system, 

93-46X  672.7  —  2116.32  X  26.60 

c= 

Substituting  the  constants  in  the  characteristic  equation 
gives: 

French  system,         pv=^i.^T—  198^.      ....     (176) 
English  system,        pv  =  93.5  T  —  97 1/* (177) 


S  UPERHEA  TED    VA  PORS.  131 

Zeuner's  constants  for  equation  (176)  differ  from  those 
given,  since  he  used  424  for  the  mechanical  equivalent  of  one 
calorie,  and  273  for  the  absolute  temperature  of  freezing- 
point. 

In  using  these  equations  for  superheated  steam  it  is  to  be 
remembered  that  the  pressures  are  specific  pressures  —  i.e.r 
kilograms  per  square  metre  or  pounds  per  square  foot  — 
whereas  the  pressures  of  saturated  steam  are  commonly  stated 
in  millimetres  of  mercury  or  in  pounds  on  the  square  inch. 

The  form  of  the  equation  lends  itself  to  the  ready  calcula- 
tion of  volume  or  temperature;  but  the  calculation  of  pressure 
can  be  made  only  by  successive  approximations. 

For  example,  the  specific  volume  of  steam  having  the 
pressure  of  IOO  pounds  by  the  gauge  and  a  temperature  of 
400°  F.  is 

v  _.  93-5^  —  9711*  __  93-5  X  860.7-971(144  x  114-7)* 
/  144  X  114-7 

.  •  .     v  =  4.20  cubic  feet. 

For  example,  the  pressure  of  superheated  steam  having  a 
temperature  of  400°  F.  and  a  specific  volume  of  5  cubic  feet 
is  approximately 

|   p  =  93^  =93.5X  860.7 

more  accurately  it  is 

93.5X860.7  - 


and  a  third  approximation  is 

93  5  X  860.7  -  97r  x 


p  = 


p  =  97.1  pounds  per  square  inch  absolute. 


*32  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Specific  Heat  at  Constant  Volume.  —  The  specific  heat 
of  superheated  steam  at  constant  volume  may  be  calculated 
by  applying  equation  (158)  to  the  case  of  saturated  steam. 
The  following  table  gives  the  values  obtained  at  several 
pressures: 

SPECIFIC    HEAT    OF   SUPERHEATED    STEAM. 

Pressures,  pounds  ) 

.    u  ••  i  5  5°        I0°          20°          3°° 

per  square  inch,    ) 

Specific  heat,  cv,  O-351      0.348     0.346        0.344        0.341 

This  table  develops  the  fact  already  mentioned  that  the 
specific  heat  of  superheated  steam  at  constant  volume, 
deduced  from  the  form  of  the  characteristic  equation  (160) 
and  the  known  properties  of  saturated  and  superheated  steam, 
is  a  variable.  This  conclusion  applies  properly  to  steam 
that  is  only  slightly  superheated,  whereas  our  experimental 
knowledge  of  the  properties  of  superheated  steam  relates  to 
steam  that  is  superheated  to  a  marked  degree. 

Intrinsic  Energy.  —  The  combination  of  the  equation 

dQ  =  A(dE+pdv) 
equation  (167)  gives 


dE  = 


an  equation  identical  in  form  with  that  for  a  perfect  gas. 

It  is  convenient  to  calculate  the  intrinsic  energy  from 
the  freezing-point  of  water,  using  a  combination  of  equation 
(178)  and  equation  (134), 


SUPERHEATED    VAPORS  133 

for  saturated  vapor.  The  increase  of  intrinsic  energy  due  to 
heating  a  liquid  from  freezing-point  to  the  temperature  /  and 
entirely  vaporizing  it  is 


The  increase  of  energy  due  to  superheating  the  vapor  under 
the  constant  pressure  /  so  that  the  specific  volume  increases 
from  that  for  saturated  steam  to  that  for  superheated  steam  is 

pv  PS     =  p(v  —  s) 

k—  i       k—  i         k—  i 

The  total  increase  of  energy  is 

I         ..'       '      *=*l£l  +  *(*  +  *•      -     -     •    079) 

Total  Heat  of  Superheated  Vapor.  —  By  the  total  heat 
of  superheated  vapor  is  meant  the  heat  required  to  change 
one  unit  of  weight  of  the  liquid  at  freezing-point  into  super- 
heated vapor  having  a  given  temperature.  It  may  be  sep- 
arated into  three  parts:  the  heat  of  the  liquid  q,  the  heat  of 
vaporization  r,  and  the  heat  required  to  superheat  the  steam, 


in  which  ts  is  the  temperature  of  the  superheated  steam  and  / 
is  the  temperature  of  saturated  steam  at  the  same  pressure. 
The  total  heat  is  consequently 


(i  80) 


Comparison  with  Experiments.  —  Experiments    on   the 
specific  volume  of  superheated  steam  were  made  by  Him,* 

*  Thdorie  M/canique  de  la  Chaleur. 


134 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


from  the  report  of  which  Zeuner  selected  the  experimental 
data  in  the  following  table.  The  specific  volume  has  been 
calculated  by  aid  of  equation  (176),  and  placed  in  the  table 
opposite  the  experimental  results  to  show  the  comparison  of 
the  characteristic  equation  with  experiments. 

SPECIFIC    VOLUME    OF    SUPERHEATED    STEAM. 


SPECIFIC  VOLUME. 

Cubic  meters. 

Pressure 
in 
atmospheres. 

Temperature. 
Centigrade. 

Hirn's 
experiments. 

Equation  (176). 

, 

118.5 

1.74 

1-75 

I 

141 

1.85 

1.87 

3 

2OO 

0.697 

0.699 

4 

165 

0.4822 

0.476 

4 

2©0 

0.522 

0.520 

4 

246 

0.5752 

0.577 

5 

162.5 

0.3758 

0.376 

5 

2O5 

0.414 

0.418 

The  table  on  the  next  page  shows  that  the  characteristic 
equation  for  superheated  steam  applies  fairly  well  to  the  limit- 
ing case  of  saturated  steam.  The  values  in  column  2  were 
taken  directly  from  the  table  of  the  properties  of  saturated 
steam,  and  the  corresponding  quantities  in  column  3  were  cal- 
culated by  aid  of  equation  (177).  The  entropies  in  column  4 
are  calculated  by  the  expression 


Column  5  is  obtained  by  calculating  by  equation  (172)  the 
change  of  entropy  from  freezing-point  to  the  given  pressure 
and  corresponding  temperature,  and  adding  it  to  the  entropy 
at  freezing-point;  the  change  of  entropy  is  negative  and  when 
added  gives  a  decreasing  value  to  the  entropy  as  the  pressure 


SUPERHEATED    VAPORS. 
APPLICATION    TO    SATURATED    STEAM. 


135 


Absolute 

Specific  Volumes, 
Cubic  Feet. 

Entropy. 

Pressure, 

Pounds  per 
Square  Inch. 

Tabular 
Value. 

Equation 
d77). 

Equation 
(MS)- 

Equation 
(172). 

i 

2 

3 

4 

5 

14.7 

26.60 

29.6 

.7484 

•752 

30 

13-59 

13.7 

.6891 

.704- 

60 

7.096 

7.12 

-6340 

.641 

IOO 

4-403 

4-38      . 

-5945 

.598 

ISO 

3.0II 

3-oo 

•5649 

.568 

200 

2.294 

2.30 

.5446 

.546 

300 

1-554 

1-57 

.5262 

•517 

Adiabatic  Line.  —  During  an  adiabatic  change  the  entropy 
remains  constant;  consequently  from  the  general  equation 
(165)  we  have 


dt 


log,  ~r  =  —  (k  —  i)  log,—  ; 
*  i  2>i 

TV*-1  =  7>*-', 


(181) 


which  is  deduced  in  the  same  way  as  the  corresponding  equa- 
tion  for  a  perfect  gas,  but  differs  in  that  k  is  an  arbitrary  con- 
stant, while  the  equation  for  perfect  gases  has  in  the  exponent 
k  the  ratio  of  the  specific  heats. 

From  equation  (166)  we  may  deduce  in  a  similar  manner 
the  equation 


Tp   «     =  T,p^~.  .     ...     .     .     (182) 

Equation  (167)  is  not  in  convenient  form  for  treatment  in 


136  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

the  manner  used   for  deducing  the  two  preceding  equations, 
but  from  those  equations  we  may  readily  deduce 

/^=A^i*»  •      •      •      ••'•'*-.••.    (183) 

which  may  be  considered  to  be  the  typical  adiabatic  equation. 
The  external  work  during  an  adiabatic  expansion  may  be 
calculated    by  an    equation    having  the    same   form  as    that 
deduced  for  perfect  gases,  i  e., 


w=r=1-l\I--\^l   }'  •  •  •  ('84) 

provided  that  the  vapor  remains  superheated  to  the  end  of 
the  expansion. 

If  a  vapor  is  not  very  strongly  superheated  it  is  liable  to 
become  saturated  and  moist  during  an  adiabatic  expansion, 
and  in  that  case  an  extension  of  the  method  used  for  a  mix- 
ture of  a  liquid  and  its  vapor  must  be  employed.  The 
increase  of  entropy  of  superheated  vapor  above  that  of  the 
liquid  at  freezing-point  may  be  divided  into  three  parts:  1st, 
that  due  to  heating  the  liquid;  2d,  that  due  to  vaporizing 
the  liquid;  and  3d,  that  due  to  superheating  the  steam.  The 
first  two  parts  have  already  been  discussed  in  the  chapter  on 
saturated  vapors;  the  third  part  is  represented  by 


"TV 


where  c  is  the  specific  heat  of  the  vapor  at  constant  pressure 
and  Ts  is  the  temperature  of  the  superheated  vapor,  while  J1, 
is  the  temperature  of  saturated  vapor  at  the  given  pressure. 
Assuming  that  the  steam  is  moist  at  the  final  pressure/,  and 
temperature  7",,  we  may  calculate  the  condition  x^  by  aid  of 
the  equation 


*  i 


S  UPERHEA  TED    VA  PORS*  137 

The  specific  heat  of  superheated  steam  is 

cp  =  0.4805. 

For  example,  let  the  initial  pressure  be  100  pounds  abso- 
lute per  square  inch  and  the  initial  temperature  be  400°  F.  ; 
required  the  condition  of  the  steam  after  an  adiabatic  expan- 
sion to  15  pounds  absolute.  Here  we  have 

t,  =  327°-6,          r,  =  884.0,          e,  =  0.4733, 
/1=2is°.o,         ^  =  965.1,          0,  =  0.3143;      . 


884.0  860.7     ., 

+  0.4733  +  0.4805  log,   -  =  :      +  0.3  143  ; 


.  •  .     x  —  0.923. 

The  external  work  for  such  an  adiabatic  expansion  is 
obtained  by  taking  the  difference  of  the  initial  and  final 
intrinsic  energies,  which  may  be  calculated  individually  by 
equations  (179)  and  (134). 

For  example,  with  the  conditions  of  the  preceding  problem 
we  have 

=  93-  5  PI  -97IA*  _  93-5  X  860.7  -  971  X  14400* 
A  14400 

=  4.85  cubic  feet. 
Consequently  the  intrinsic  energy  is 


.4400(4.85-4.403) + 778(297  9 + 802  8)  =  875700  ft  Jbs 


138  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  final  intrinsic  energy  is 


£*  =  778(0.  +  *,PS)  =  778(i8i.8  +  0.923  X  892.6) 
=  782400  foot-pounds. 

so  that  the  external  work  is 

El  —  E^  —  875700  —  782400  =  93300  foot-pounds. 

Isoenergic  Line.  —  The  equation  to  this  line  is  obtained 
from  equation  (178)  by  making  E  equal  to  £19  so  that 


(i  86) 


which,  like  the  isoenergic  line  for  a  perfect  gas,  is  the  equa- 
tion to  a  rectangular  hyperbola. 

The  external  work  during  an  isoenergic  expansion  is 

r  v*  P 

W  =    I  pdv  =  p.v  log.—  =  p.v.  log/— .       .     (187) 
J  J  i>i  A 

Since  all  the  heat  applied  is  expended   in  external  work, 
Q  =  AW.    .     .     .     .    .     .     .     (188) 

Isothermal  Line. — The  equation  to  the  isothermal  line 
for  a  superheated  vapor  is  obtained  by  making  T  a  constant 
in  the  characteristic  equation 


so  that 

~ .     .    .    .    (189) 


SUPERHEATED    VAPORS.  139 

The  heat  applied  during  an  isothermal  change  is  obtained 
by  integrating  equation  (166)  with  T  constant,  giving 


(190) 


But  we  have  in  general 

Q  =  A(E,-E,+ 

so  that  the  external  work  is 


W  '  —  —  -I-  F  --  F 
~         *      l         *' 


which  may  be  reduced  by  equations  (190)  and  (178)  to 


Properties  of  Sulphur  Dioxide. — One  of  the  most  inter- 
esting and  important  applications  of  the  theory  of  superheated 
vapors  is  found  in  the  approximate  calculation  of  properties 
of  certain  volatile  liquids  which  are  used  in  refrigerating- 
machines,  and  for  which  we  have  not  sufficient  experimental 
data  to  construct  tables  in  the  manner  explained  in  the 
chapter  on  saturated  vapors. 

For  example,  Regnault  made  experiments  on  the  pressures 
of  saturated  sulphur  dioxide,  ammonia,  and  carbon  dioxide, 
but  did  not  determine  the  heat  of  the  liquid  nor  the  total 
heat.  He  did,  however,  determine  some  of  the  properties  of 
these  substances  in  the  gaseous  or  superheated  condition, 
from  which  it  is  possible  to  construct  the  characteristic  equa- 
tions for  the  superheated  vapors.  These  equations  can  then 
be  used  to  make  approximate  calculations  of  the  saturated 
vapors,  for  such  equations  are  assumed  to  be  applicable  down 


140  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

to  the  saturated  condition.  Of  course  such  calculations  are 
subject  to  a  considerable  unknown  error,  since  the  experi- 
mental data  are  barely  sufficient  to  establish  the  equations  for 
the  superheated  vapors. 

The  specific  heat  of  gaseous  sulphur  dioxide  is  given  by 
Regnault  *  as  0.15438,  and  the  coefficient  of  dilatation  as 
0.0039028.  The  theoretical  specific  gravity  compared  with 
air,  calculated  from  the  chemical  composition,  is  given  by 
Landolt  and  Bornstein  f  as  2.21295.  Gmelin  £  gives  the 
following  experimental  determinations:  by  Thomson,  2.222; 
by  Berzelius,  2.247.  The  figure  2. 23  will  be  assumed  in  this 
work,  which  gives  for  the  specific  volume  at  freezing-point 
and  at  atmospheric  pressure 


0.7735327 

-  ^^-^  =  0.347  cubic  metres. 


The  corresponding  pressure  and  temperature  are  10333 
273°.;  C. 

Now  the  coefficient  of  dilatation  is  the  ratio  of  the  increase 
of  volume  at  constant  pressure,  for  one  degree  increase  of 
temperature,  to  the  original  volume.  Writing  the  equation 
(160)  in  the  following  form, 

Pv  =  CAaT-  CPa> •     (J92) 

and  applying  it  at  o°  C.  and  i°  C.,  we  have 


*  Memoir es  de  V  Institut  de  France t  tome  xxi,  xxvi. 
\  Physikalische-chemische  Tabellcn. 
j  Watt's  translation,  p.  280. 


SUPERHEATED    VAPORS.  141 


Substituting  the  known  values  and  solving  for  #,  we 
obtain  0.212;  but  the  equation  obtained  from  the  equation 
(192)  with  this  figure  does  not  agree  well  with  Regnault's 
experiments  on  the  compressibility  of  sulphur  dioxide.  If, 
instead,,  we  make 

a  ==  0.22, 

then  by  equation  (192)  the  coefficient  of  dilatation  becomes 
0.00404,  and  it  will  be  shown  later  that  the  equation  deduced 
with  this  value  agrees  quite  well  with  the  experiments  on 
compressibility. 

The  coefficient  of  T  in  equation  (192)  is  therefore 

0.15438  X  426.9  X  0.22  =  14.5, 
and  the  coefficient  of  pa  is 

H.5X  273.7-  10333  X  0.347  =  48nearly. 


so  that  the  equation  becomes 

pv=  14.5  T-48/0-22.    .....     (193) 

Regnault  found  for  the  pressures 

A  =    697.83  mm.  of  mercury, 
A  =  1341-58    "      "      " 

and  at  7°.  7  C.  the  ratio 

-^  =  1.02088. 


142  THERMODYNAMICS   Of    THE   STEAM-ENGINE. 

Reducing  the  given  pressures  to  kilograms  on  the  square 
metre,  and  the  temperature  to  the  absolute  scale,  and  applying 
to  equation  (192),  we  obtain  1.016  instead  of  the  experi- 
mental value  for  the  above  ratio. 

Regnault  gives  for  the  pressure  of  saturated  sulphur  diox- 
ide, in  mm.  of  mercury,  the  equation 

log/  =  a  —  ban  —  cfin  ; 

a  =  5.6663790  ; 
log  £  =  0.479242  5; 
log  c  =  9.1659562  —  10  ; 
log  a  =  9.9972989  —  10  ; 
log/?  =  9.98729002  —  10  ; 

n  =  t  +  28°  C. 

Applying  equation  (no),  page  92,  to  this  case, 


-  = 

log  a  =  9.9972989  ; 
log/?  =  9.98729002  ; 

=  8.6352146; 

=  7.9945332; 

n  =  t  +  28°  C. 

i 

The  specific  volume  of  saturated  sulphur  dioxide  may  be 
calculated  by  inserting  in  equation  (193)  for  the  superheated 
vapor  the  pressures  calculated  by  aid  of  the  above  equation. 
The  results  at  several  temperatures  are  as  follows: 

/         -30°C.  o.  +30°C. 

s          0.8292  0.2256  0.0825 

Andreeff  *  gives  for  the  specific  gravity  of  fluid  sulphur 

*  Ann.  Chem.  PAarm.,  1859. 


SUPERHEATED    VAPORS.  1  43 

dioxide    1.4336;    consequently    the    specific    volume   of    the 
liquid  is 

<r  =  0.0007. 

The  value  of  r,  the  heat  of  vaporization,  may  now  be  cal- 
culated at  the  given  temperatures  by  equation  (128),  page  104, 


in  which  u  =  s  —  <r. 

The  results  are 

/         —  30°  C.  o  +  30°  C. 

r  106.9  97.60  90.  54 

Within  the  limits  of  error  of  our  method  of  calculation, 
the  value  of  r  may  be  found  by  the  equation 

r  =  98  -  0.27/  .......     (194) 

To  find  the  specific  heat  of  the  liquid  we  may  use  equa- 
tion (174),  page  129, 

T     dp\  dr         r 


At  o°  C.  the  specific  heat  is  approximately 

c  =  0.4. 

In  English  units  we  have  for  superheated  sulphur  dioxide 
pv  =  26.4T  -I84/0-22,   .    -.    .    .     .     (195) 


144  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

the  pressures  being  in  pounds  on  the  square  foot,  the  volumes 
in  cubic  feet,  and  the  temperatures  in  Fahrenheit  degrees 
absolute. 

For  pressures  in  pounds  on  the  square  inch  at  tempera- 
tures on  the  Fahrenheit  scale. 

log  p  —  a  —  bot*  —  cfi*  ; 

«  =  3-9527847  ; 

log  b  =  0.4792425  ; 
log  c  =  9.1659562  —  10  ; 
log<*  =  9.9984994-  10  ; 
log  ft  =  9.99293890  -  10  ; 
»=/+  i8°.4F. 

For  the  heat  of  vaporization 

r  =  176  -  0.27(*  -  32),      ....     (196) 
and  for  the  specific  heat  of  the  liquid 

c  =  0.4. 

In  applying  these  equations  to  the  calculation  of  a  table 
of  the  properties  of  saturated  sulphur  dioxide  the  pressures 
corresponding  to  the  temperatures  are  calculated  as  usual. 
Then  the  heat  of  the  liquid  is  calculated  by  aid  of  the  con- 
stant specific  heat.  The  heat  of  vaporization  is  calculated  by 
aid  of  equation  (196).  Next  the  specific  volume  is  calculated 
by  inserting  the  given  temperature  and  the  corresponding 
pressure  for  the  saturated  vapor  in  the  characteristic  equation 
(193)  or  (195).  Having  the  specific  volume  of  the  vapor  and 
that  of  the  liquid,  the  heat  equivalent  (Apu)  of  the  external 
work  is  readily  found.  Finally,  the  entropy  of  the  liquid  is 
calculated  by  the  equation 


(197) 


SUPERHEATED    VAPORS.  145 

Properties  of  Ammonia.  —  The  specific  heat  of  gaseous 
ammonia,  determined  by  Regnault,  is  0.50836.  The  the- 
oretical specific  gravity  compared  with  air,  calculated  from 
the  chemical  composition,  is  given  by  Landolt  and  Bornstein 
as  0.58890.  Gmelin  gives  the  following  experimental  deter- 
minations: by  Thomson,  0.5931  ;  by  Biot  and  Arago,  0.5967. 
For  this  work  the  figure  0.597  will  be  assumed,  which  gives 
for  the  specific  volume  at  freezing-point  and  at  atmospheric 
pressure 

0.77^5327 
v0  =  =1.30  cubic  metres. 

The  coefficient  of  dilatation  has  not  been  determined,  and 
consequently  cannot  be  used  to  determine  the  value  of  a  in 
equation  (192).  It,  however,  appears  that  very  consistent 
results  are  obtained  if  a  is  assumed  to  be  J,  as  for  super- 
heated steam.  The  coefficient  of  T  then  becomes 

0.50836  X  426.9  X  i  =  54-3, 
and  the  coefficient  of/*  is 

54.3X273.7-  IQ333  X  1.30. 

i  —  ~  —  i42  » 

10333* 

so  that  the  equation  becomes 

pv=  54-3^-  142/j  ......     (198) 


The  coefficient  of  dilatation,  calculated  by  the  same 
process  as  was  used  in  determining  a  for  sulphur  dioxide,  is 
0.00404,  which  may  be  compared  with  that  for  sulphur 
dioxide. 

Regnault  found  for  the  pressures 

pl  =    703.50  mm.  of  mercury, 
A  =  H35.3      "       " 


146  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and  at  8°.  I  C.  the  ratio 

^  =  1.0188, 
Pf>* 

while  equation  (198)  gives  under  the  same  conditions  1.0200. 
For  saturated  ammonia  Regnault  gives  the  equation 

log  p  —  a  —  ban  —  c/3"  ; 

a  =  11.5043330; 
log  b  —  0.8721769; 
log  c  =  9-9777087  —  10  ; 
log  a  =  9.9996014  —  10  ; 
log  ft  =  9.9939729  —  10  ; 

n  =  t+  22°  C.  ; 

by  aid  of  which  the  pressures  in  mm.  of  mercury  may  be  cal- 
culated for  temperatures  on  the  centigrade  scale.  The 
differential  coefficient  may  be  calculated  by  aid  of  the  equa- 
tion 


log  A  =  8.1635170  —  10  ; 
Iogj5  =  8.4822485  —  10  ; 
log  a  =  9.9996014  —  10; 
log  ft  =  9.9939729  -  10  ; 

n  =  /+  22°  C. 

The  specific  volume  of  saturated  ammonia  calculated  by 
equation  (198)  at  several  temperatures  are 

t         -  30°  C.  o  +  30°  C. 

s          0.9982  0.2961  0.1167 

Andreeff  gives  for  the  specific  gravity  of  liquid  ammonia 
at  o°  C.  0.6364,  so  that  the  specific  volume  of  the  liquid  is 

a  —  0.0016. 


SUPERHEATED    VAPORS.  147 

The  values  of  r  at  the  several  given  temperatures,  calcu- 
lated by  equation  (128),  are 

/          -  30°  C.  o  +  30°  C. 

r  325.7  300.15  277.5 

which  may  be  represented  by  the  equation 

r  =  300  —  o.8/ (J99) 

The  specific  heat  of  the  liquid,  calculated  by  aid  of  equa- 
tion (129),  is 

c  =  i.i. 

In  English  units  the  properties  o    superheated  or  gaseous 
ammonia  may  be  represented  by  the  equation 

pv  —  99^—  540/i, (200) 

in  which  the  pressures  are  taken  in  pounds  on  the  square  foot 
and  volumes  in  cubic  feet,  while  T  represents  the  absolute 
temperature  in  Fahrenheit  degrees. 

The  pressure  in  pounds  on  the  square  inch  may  be  calcu- 
lated by  the  equation 

log  /  =  a  —  ban  —  cfin  ; 

a  =  9.79P7380 ; 
log  b  =  0.8721769  —  10  ; 
log£  =9-9777o87—  10 ; 
log  a  =  9.9997786  -  10  ; 
log  fi  =  9.99665 16  —  10  ; 

n  =  t+  7°.6  F. 

The  heat  of  vaporization  may  be  calculated  by  the  equa- 
tion 

r  =  540  -  o.8(/  -  32), (201) 

and  the  specific  heat  of  the  liquid  is 

c  =  i.i. 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


EXAMPLES. 

1.  What  is  the  weight  of  one  cubic  foot  of  superheated 
steam  at  500°  F.  and  at  60  pounds  pressure  absolute  ? 

Ans.  0.107  lb. 

2.  Superheated  steam  at  50  pounds  absolute  has  half  the 
density  of  saturated  steam  at  the  same  pressure.     What  is  the 
temperature  ?  Ans.   930°. 8  F. 

3.  Find  the  increase  of  intrinsic  energy  and  increase  of 
entropy  of  a  pound  of   superheated    steam,   at    100   pounds 
absolute  and   at  400°  F.,  above  the  values  at   32°  for  water. 

Ans.   876400  ft.-lbs.  and  1.6369. 

4.  Find  the  external  work  of  one  kilogram   of  steam  in 
expanding  adiabatically  from   the   pressure  of   3000  mm.   of 
mercury   and   the   temperature    300°   C.    to   the   pressure   of 
20*00  mm.       Find    also   the   final   temperature  and   volume. 

Ans.   (i)  7690  m-kgs. ;  (2)  244°. 7  C. ;  (3)  0.8842  eu.  ft.  - 

5.  In  example  4  find  the  external  work  for  an  isothermal 
expansion  from  the  initial  condition  to  the  final  volume  as 
determined  in  that  example.  Ans.  8120  m.-kgs. 

6.  Let  the  initial  temperature  of  superheated  steam  be 
380°  F.  at  the  pressure  of    150  pounds  absolute.      Find  the 
condition   after  an  adiabatic  expansion   to  20  pounds  abso- 
lute.     Determine  also  the  initial  and  final  volumes. 

Ans.   (i)  0.8953;  (2)  3.094  cu.  ft.;   (3)  17.83  cu.  ft. 

7.  In  example  9,   page    122,  suppose  that  the  steam  at 
cut-off  were   superheated   10°   F.   above  the  temperature  of 
saturated  steam  at  the  given  pressure,  and  solve  the  example. 

Ans.    (i)    0.8865;    (2)    79°. 5    superheating;   (3)   same   as 
before;  (4)  n  =  1.137;   (5)  1972  and  1950  ft.-lbs. 


CHAPTER  VIII. 

FLOW   OF   FLUIDS. 

• 

ONE  of  the  most  important  problems  in  thermodynamics 
is  to  find  the  amount  of  a  gas  or  a  vapor  which  will  be  dis- 
charged through  a  given  orifice  in  a  unit  of  time.  To  make 
the  statement  of  the  problem  more  concrete  it  will  be  sup- 
posed that  the  fluid  passes  from  the 
large  cylinder  A  (Fig.  30)  into  the  I*""]"]  [, 

smaller  cylinder  B  through  a  well- 
rounded  orifice  at  C.  The  cylinders 
will  be  supposed  each  to  be  at  the 

same  temperature  as  the  fluid  in  it,  so  that  there  will  be  no 
communication  of  heat  to  or  from  the  walls  of  the  cylinders. 

The  process  is  clearly  non-reversible,  so  that  only  the  first 
law  of  thermodynamics  can  be  used,  and,  as  in  equation  (43), 


ILJPi 


dQ  =  A(dE  +  dW  +  dK}, 

a  term  must  be  added  to  represent  the  kinetic  energy  due  to 
ordinary  motion  of  translation. 

Let  it  be  supposed  that  there  is  a  frictionless  piston  in 
each  cylinder;  the  piston  in  A  exerts  the  pressure  pl  on  the 
fluid  in  front  of  it,  and  the  piston  in  B  has  on  it  the  fluid 
pressure  /2.  Each  unit  of  weight  of  fluid  passing  from  A 
through  the  orifice  has  the  work  plvl  done  on  it,  while  each 
pound  entering  the  cylinder  B  does  the  work  pjv%  .  The 
assumption  of  pistons  is  merely  a  matter  of  convenience,  and 
if  they  are  suppressed  the  same  conditions  with  regard  to 
external  work  will  hold. 

149 


ISO  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

If   the  velocity  in  A  is  Vl  the  kinetic  energy  of  one  unit 

Fa 
of  weight  in  that  cylinder  is  — ;  the  kinetic  energy  in  B  is 

o 

V 

— -  for  a  velocity  F. 

*g 

The  intrinsic  energies  in  A  and  .#  are  £,  and  £2.  If  there 
is  no  heat  communicated  to  or  from  the  fluid  the  sum  of  the 
intrinsic  energy,  external  work,  and  kinetic  energy  must 
remain  constant,  so  that 


(202) 


this  is  the  fundamental  equation  for  the  flow  of  a  fluid. 

It  is  proper  to  include  a  term  for  the  gain  or  loss  of  heat 
at  the  orifice,,  which  is  commonly  made  of  metal  and  is  in 
metallic  contact  with  the  walls  of  the  cylinders,  and  will  not 
have  the  temperature  of  the  fluid  in  it;  but  the  amount  of 
heat  that  can  be  communicated  to  the  fluid  at  the  orifice  is 
too  small  to  take  account  of,  consequently  the  term  is  not  put 
into  the  fundamental  equation. 

Usually  the  velocity  in  the  large  cylinder  A  is  small  and 
the  term  depending  on  it  may  be  neglected.  Solving  for  the 
term  depending  on  the  velocity  in  B  and  dropping  the  sub- 
script, we  have 

^=  £,-£,+ A", -A*V    -     -     -     (203) 

Incompressible  Fluids. — There  is  little  if  any  change  of 
volume  or  of  intrinsic  energy  in  a  liquid  in  passing  through 
an  orifice  under  pressure,  so  that  the  equation  of  flow  becomes 
in  this  case 

F' 

=  (A-/>, (204) 


FLO  W   OF  FLUIDS.  151 

If  the  difference  of  pressure  is  due  to  a  difference  of  level 
or  head,  h,  we  have 

A  -  A  =  ky> 

where  x  is  the  density,  or  weight  of  a  unit  of  volume,  and  is 
the  reciprocal  of  the  specific  volume;  consequently  equation 
(204)  reduces  to 

F3 

•       =  *      .......    (2°5) 


which  is  the  usual  equation  for  the  flow  of  a  liquid  through  a 
small  orifice. 

Flow  of  Gases.  —  The  intrinsic  energy  of  a  unit  of  weight 
of  a  gas  is 


so  that  the  equation  for  the  flow  of  a  gas  is 
Fa         AV,         A^t 

-^  =  fe  -  ^i  +A",  -/A: 
•••    ^-^^(A^-A^)  .......    (206) 

For  an  adiabatic  transformation 

/,»,"=  A*,":     .........     (207) 


so  that  equation  (206)  may  be  reduced  to 

-     .    .    .    (208) 


152  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

If  the  area  of  the  orifice  is  #,  then  the  volume  discharged 
per  second  is 


and  the  weight  discharged  per  second  is 


aV 

w  =  --  , 


where  vt  is  the   specific   volume   at   the  lower  pressure  /a. 
Substituting  for  V  from  equation  (208)  and  for  z/a  from  (207), 


But  from  the  characteristic  equation 


so  that 


The  equations  deduced  for  the  flow  of  air  apply  to  the 
flow  from  a  large  cylinder  or  reservoir  into  a  small  straight 
tube  through  a  rounded  orifice.  The  lower  pressure  is  the 
pressure  in  the  small  tube  and  differs  materially  from  the 
pressure  of  the  space  into  which  the  tube  may  deliver.  In 
order  that  the  flow  shall  not  be  affected  by  friction  against 
the  sides  of  the  tube  it  should  be  short — not  more  than  once 


FLOW  OF  FLUIDS.  153 

or  twice  its  diameter.  The  flow  does  not  appear  to  be 
affected  by  making  the  tube  very  short,  and  the  degree  of 
rounding  is  not  important  ;  the  equations  for  the  flow  of  both 
air  and  ^team  may  be  applied  with  a  fair  degree  of  approxi- 
mation to  orifices  in  thin  plates  and  to  irregular  orifices. 

Professor  Fliegner*  made  a  large  number  of  experiments 
on  the  flow  of  air  from  a  reservoir  into  the  atmosphere,  with. 
pressures  in  the  reservoir  varying  from  808  mm.  of  mercury 
to  3366  mm.  He  used  two  different  orifices,  one  4.085  and 
the  other  7.314  mm.  in  diameter,  both  well  rounded  at  the 
entrance. 

He  found  that  the  pressure  in  the  orifice,  taken  by  means 
of  a  small  side  orifice,  was  0.5767  of  the  absolute  pressure  in 
the  reservoir  so  long  as  that  pressure  was  more  than  twice 
the  atmospheric  pressure;  under  such  conditions  the  pressure 
in  the  orifice  is  independent  of  the  pressure  of  the  atmosphere. 

If  the  ratio  -  is  replaced  by  the  number  0.5767  and  if  K  is 

replaced  by  its  value  1.405  in  equation  (210)  we  shall  have 
for  the  equation  for  the  flow  of  a  gas 


the  flow  into  the  atmosphere  from  a  reservoir  having 
a  pressure  less  than  twice  the  atmospheric  pressure  Fliegner 
found  the  empirical  equation 


(2I2) 


where  pa  is  the  pressure  of  the  atmosphere. 

These  equations  were  found  to  be  justified  by  a  compari- 
son with  experiments  on  the  flow  of  air,  made  by  Fliegner 
himself,  by  Zeuner,  and  by  Weisbach. 

*  Der  Civilingenieur,  vol.  xx,  p.  14,  1874. 


1 54  THERMOD  YNA  MICS   OF   THE   S  TEA  M-ENGINE. 

Although  these  equations  were  deduced  from  experiments 
made  on  the  flow  of  air  into  the  atmosphere,  it  is  probable 
that  they  may  be  used  for  the  flow  of  air  from  one  reservoir 
into  another  reservoir  having  a  pressure  differing  from  the 
pressure  of  the  atmosphere. 

Fliegner's  Equations  for  Flow  of  Air. — Introducing  the 
values  for  g  and  R  in  the  equations  deduced  by  Fliegner,  .we 
have  the  following  equations  for  the  French  and  English 
systems  of  units: 

French  units. 


P,  <2pa,         W  =  0. 


English  units. 

A 


w  =  0.5300 


w  = 


/x  =  pressure  in  reservoir; 

pa  =  pressure  of  atmosphere  ; 

7^  =  absolute  temperature  of  air  in  reservoir  (degrees  centi- 

grade,   French    units;     degrees   Fahrenheit,    English 

units). 

In  the  English  system/!  and  pa  are  pounds  per  square 
inch,  and  a  is  the  area  of  the  orifice  in  square  inches,  while 
w  is  the  flow  of  air  through  the  orifice  in  pounds  per  second. 
If  desired,  the  area  may  be  given  in  square  feet  and  the  pres- 
sures in  pounds  on  the  square  foot,  as  is  the  common  conven- 
tion in  thermodyanmics. 


FLOW   OF  FLUIDS.  155 

In  the  French  system  w  is  the  flow  in  kilograms  per 
second.  The  pressures  may  be  given  in  kilograms  per  square 
metre  and  the  area  a  in  square  metres;  or  the  area  may  be 
given  in  square  decimetres  or  square  centimetres,  and  the 
pressures  in  kilograms  on  the  same  unit  of  area  used  in  con- 
nection therewith.  If  the  pressures  are  in  millimetres  of 
mercury,  multiply  by  13.5959;  if  in  atmospheres  multiply 
by  10333. 

Theoretical  Maxima.  —  It  is  interesting  to  investigate  the 
conditions  that  give  the  maximum  discharge  of  air  as  calcu- 
lated by  equation  (2  10),  neglecting  for  the  moment  Fliegner's 
experimental  limit  of  the  ratio  of  pressures.  For  this  purpose 
we  may  equate  to  zero  the  first  differential  coefficient  of  the 
weight  with  regard  to  the  pressure  /,  ,  assuming  pl  to  be 
constant.  The  variable  term  is 


A          A- 


and  the  result  of  equating  to  zero  the  differential  coefficient 
of  this  expression  with  regard  to  /,  is 


a  number  which  is  somewhat  less  than  Fliegner's  experimen- 
tal ratio. 

There  is  no  algebraic  maximum  to  the  velocity  of  flow  as 
calculated  by  equation  (208),  but  the  kinetic  theory  of  gases 
gives  a  theoretical  limit  to  the  velocity,  for  which  the  follow- 
ing statement  is  given  by  Joule.* 

Maximum  Velocity  of  Flow.  —  According  to  the  kinetic 
theory  of  gases,  the  pressure  of  a  gas  on  the  walls  of  the  con- 
taining vessel  is  due  to  the  impact  of  the  molecules  of  the 
gas.  To  estimate  the  mean  velocity  of  the  molecules  Joule 

*  Memoir  Phil.  Soc.,  vol.  ix,  p.  107. 


156  THERMODYNAMICS   OF   THE   STEAM-ENGINE, 

proceeds  in  the  following  manner:  The  weight  of  one  cubic 
metre  of  gas  is  —  ,  and  the  pressure  which  it  exerts  on  each  of 
the  six  sides  of  a  cubical  vessel  containing  it  is  p.  Suppose 
that  the  weight  -  of  the  gas  to  be  divided  into  three  equal 

portions,  one  of  which  oscillates  between  each  pair  of  faces  of 
the  cube  and  produces  the  pressure  by  impact,  first  on  one 
and  then  on  the  other  of  the  pair.  Now  if  a  body  have  a 
velocity  equal  to  g  it  will  be  brought  to  rest  by  a  force  equal 
to  its  weight  acting  on  it  for  one  second  ;  and  that  force  act- 
ing for  two  seconds  will  bring  it  to  rest  and  then  impart  to  it 
the  same  velocity  in  the  opposite  direction.  In  two  seconds 
there  will  be  g  impacts  on  each  of  the  pair  of  faces,  and  it 
will  be  assumed  that  the  effect  of  the  impacts  is  equal  to  that 

of  a  pressure  equal  to  —  —  kilograms  on  each  face;  that  is,  on 

one  square  metre.  The  pressure  will  vary  as  the  square  of 
the  velocity,  since  both  the  force  required  to  reverse  the 
velocity  and  the  number  of  impacts  increase  with  the  velocity. 
Finally,  Joule  makes 


in  which  u  is  the  mean  velocity  of  the  molecules  of  the  gas. 
This  may  be  written 


From  this  discussion  Fliegner  assumes  that  the  maximum 
velocity  of  flow  of  gas  through  an  orifice  by  the  kinetic  theory 
of  gases  is 


=  16.94/7; 


FLOW  OF  FLUIDS.  157 

for  French   units.      But  his  limiting  ratio  of  pressures  —  = 
0.5767  inserted  in  equation  (208)  gives 

Fmax  =  17. 


Flow  of  Saturated  Vapor.  —  For  a  mixture  of  a  liquid 
and  its  vapor  equation  (134)  gives 


so  that  equation  (202)  gives  for  the  adiabatic  flow  from  a 
receptacle  in  which  the  initial  velocity  is  zero 

F*       i 

—  =  ^-  (ft  -  ft  +  *,A  -  **P*)  +A».  -  A*V      •    (213) 

Substituting  for  z>,  and  z/2  from 

v  =  xu  +  cr, 
F' 
2^  ~~  ^l        ^ 

But 

p  +  .4/«  =  r; 

J79  _ 
A—      xf,~  *S.  +  &      4 

The  last  term  of  the  right-hand  member  is  small,  and  fre- 
quently can  be  omitted. 

The  value  of  xt  can  be  determined  by  the  equation 


or,  if  the  proper  tables  are  lacking,  we  may  use  the  approxi- 
mate form 


158  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

It  is  necessary  to  remember  that  while  the  tables  com- 
monly give  the  pressure  in  pounds  on  the  square  inch,  or  in 
atmospheres,  etc.,  pv  and  /a  in  the  last  term  of  equation  (214) 
are  the  specific  pressures;  that  is,  the  pressures  in  pounds  on 
the  square  foot,  or  kilograms  on  the  square  metre. 

The  weight  of  fluid  that  will  pass  through  an  orifice  hav- 
ing an  area  of  a  square  metres  or  square  feet  may  be  calcu- 
lated by  the  formula 


(215) 


The  equations  deduced  are  applicable  to  all  possible  mix- 
tures of  liquid  and  vapor,  including  dry  saturated  steam  and 
pure  hot  water.  In  the  first  place  steam  will  be  condensed 
in  the  tube,  and  in  the  second  water  will  be  evaporated. 

If  steam  blows  out  of  an  orifice  into  the  air,  or  into  a  large 
receptacle,  and  comes  to  rest,  the  energy  of  motion  will  be 
turned  into  heat  and  will  superheat  the  steam.  Steam  blow- 
ing into  the  air  will  be  wet  near  the  orifice,  superheated  at  a 
little  distance,  and  if  the  air  is  cool  will  show  as  a  cloud  of 
mist  further  from  the  orifice. 

Rankine's  Equations.  —  After  an  investigation  of  the 
experiments  made  by  Mr.  R.  D.  Napier  on  the  flow  of  steam 
Rankine  concludes  that  the  pressure  in  the  orifice  is  never 
less  than  the  pressure  which  gives  the  maximum  weight  of 
discharge,  and  that  the  discharge  in  pounds  per  second  may 
be  calculated  by  the  following  empirical  equations: 


— 


in  which  pv  is  the  pressure  in  the  reservoir,  pa  is  the  pressure 
of  the  atmosphere,  both  in  pounds  on  the  square  inch,  and  a 
is  the  area  in  square  inches. 


FLOW   OF  FLUIDS. 


159 


The  error  of  these  equations  is  liable  to  be  about  two  per 
cent;  but  the  flow  through  a  given  orifice  may  be  known  more 
closely  if  tests  are  made  on  it  at  or  near  the  pressure  during 
the  flow,  and  a  special  constant  is  found  for  that  orifice. 

Experiments  on  Flow  of  Steam. — The  results  of  tests 
made  on  the  flow  of  steam  through  orifices  or  short  tubes 
with  well-rounded  entrances,  by  Mr.  W.  H.  Kunhardt  *  in 
the  laboratories  of  the  Massachusetts  Institute  of  Technology, 
are  given  in  the  following  table: 

FLOW  OF   STEAM    THROUGH    SHORT   TUBES   WITH    ROUNDED 

ENTRANCES. 
Diameters  0.25  of  an  inch. 


05 

Pressure  above  At 
mosphere,  Pounds 
per  Square  Inch. 

Ratio  of 
Absolute 
Pressures. 

1 

c 

Flow  in  Pounds 
per  Hour. 

a 
•2* 

•g 

c 

V 

c 

V 

1 

u 

3 

i>   '    . 

"O   c£   3> 

. 
rf.r; 

31 

II 

•2H 

_o 

'ex. 

S  = 

u 

sT 

^ 

3 

H 
"o 

3 

C 

s 

c 

1 
•5 

he  Tubi 

£» 

o£ 

{! 

>l 

& 

a  o 
v  w    • 

-     -  -1 

ature  of 
Fahre 

Is 
•si 

s 
§1 

4i 

HI 

'•*  -. 

A   3 
1% 

"o 

1' 

.2 

H 

4J 

1 

| 

rt  O 

E-o 

li 

||| 

Hi 

II 

Ij 

l-f 

!| 

i§ 
*»•- 

'-- 

J 

Q 

so. 

<M 

pa 

£ 

flu 

H 

£ 

ca 

u 

&* 

o  — 
U 

i 

V.5 

3° 

74-1 

i4.8 

41.2 

'4.7 

0.332 

0.630'  126.2 

1.2 

221.0 

217.0 

224 

.018 

*  * 

30 

71.0 

13-2 

39-6 

i4.8 

0.326 

Q    634|     138.7 

1.5 

213.0 

207.8 

2i5 

.025 

3 
4 

1 

20 

20 

72.6 
75-9 

19.7 
20.4 

40  6 
42.6 

14-7 

»4  7 

0.394 
0.387 

0.634 
0.632 

141.4 
139.8 

0-5 
0.7 

216.0 
228  o 

211.4 
219.3 

220 
227 

.022 
.040 

5 

' 

2O 

71.9 

24-5 

40.6 

14-7 

0.454 

0.638 

140  6 

0.7 

213.0 

209.7 

218 

.016 

6 

0.5 

30 

72.8 

14.8 

39.0 

14-8 

0.338 

0614 

138.7 

0-3 

225.0 

2.3.6 

221 

•053 

7 

* 

20 

72.1 

20.4 

38.8 

14-8 

0.405 

O.6l7 

142.2 

o-5 

223.5 

211.7 

219 

.056 

8 

' 

30 

72.6 

24-7 

39.0 

14.8 

0.452 

0.616 

144.0 

223.0 

213.1 

220 

.046 

9 

' 

30 

73-1 

29.9 

39-2 

14  8 

0.509 

o  615 

145.2 

05 

225-5 

213.0 

222 

•054 

ID 

0.25 

3° 

72.6 

24.8 

36-1 

14.9 

0.454 

0.583 

143.8 

0.4 

225.0 

2«3-5 

220 

•054 

II 

30 

72.6 

19.9 

36-1 

14.9 

0.398 

0.583 

141  .6 

°-4 

225.0 

213.5 

220 

•054 

12 

" 

30 

72.7 

14-9 

36-2 

14.8 

0-339 

0.583 

140.5 

°-4 

227.0 

213.0 

220 

.066 

'3 

" 

30 

126.3 

27.8 

69.0 

•14.7 

0.295 

0-594 

155.0 

o-5 

358.8 

338.9 

355 

.058 

14 

125.0 

40.8 

67.9 

14.7 

0.398 

0.598 

157.0 

0.2 

355-0 

334-8 

352 

.000 

The  following  table  gives  the  results  of  some  experiments 
on  the  flow  of  steam  through  an  orifice  0.25  of  an  inch  in 
diameter,  in  a  thin  plate,  made  by  Mr.  G.  P.  Aborn  f  in  the 
laboratories  of  the  Massachusetts  Institute  of  Technology: 


*  Transactions  Am.  Soc.  Meek.  Engs.t  vol.  xi,  p.  187. 
f  Thesis,  1886. 


160 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


FLOW   OF   STEAM    THROUGH    AN    ORIFICE. 


Number  of 
Experiment. 

Higher 
Pressure. 

Difference  of 
Pressure. 

Flow  in  Pounds 
per  Hour  by 
Experiment. 

I 

71.8 

0.92 

29.7 

2 

71-5 

1.85 

43-1 

3 

71.9 

2.79 

52.6 

4 

71.6 

3-89 

67.6 

5 

71.9 

5-55 

77-6 

6 

71.8 

6.50 

84.2 

7 

71.7 

8.07 

91.8 

8 

72.9 

9-23 

93-9 

9 

72.5 

12.8 

110.3 

10 

73-7 

15-9 

124.9 

ii 

72.7 

21.  1 

I4I.5 

12 

74.2 

27.O 

156.8 

13 

71.9 

33-7 

166.3 

14 

74-3 

41.0 

180.7 

15 

72.7 

49-2 

187.7 

76 

72.9 

57-o 

195.8 

17 

73-7 

64.4 

196.9 

18 

72.0 

68.4 

197.8 

Flow  of  Superheated  Steam.  —  The  form  of  the  equation 
for  the  change  of  intrinsic  energy  of  superheated  steam  is  the 
same  as  for  a  perfect  gas,  i.e., 


>,  —     ,  =  ~,  -  —  -,  -  » 
k  —  I        k  —  I 

and  consequently  the  equations  for  the  velocity  of  flow  and 
the  weight  of  the  discharge  can  be  deduced  in  much  the  same 
form  as  for  a  perfect  gas,  provided  that  the  steam  remains 
superheated.  Though  there  are  no  experiments  on  the  flow 
of  superheated  steam  under  such  conditions,  it  is  probable 
that  the  ratio  of  the  pressures  in  the  orifice  and  in  the  reservoir 
is  something  between  0.57  and  0.6. 

But  steam  is  seldom  sufficiently  superheated  to  avoid  con- 
densation during  adiabatic  flow  through  an  orifice.  If  the 
steam  becomes  moist  in  the  orifice,  then  the  intrinsic  energy 
at  the  initial  condition  must  be  found  from  equation  (179), 
which  may  be  written 


FLOW  OF  FLUIDS.  l6l 

while  the  intrinsic  energy  at  the  pressure  in  the  orifice  is  given 
by  the  equation  for  saturated  steam, 


(217) 


so  that  the  equation  for  the  velocity  of  flow  becomes 

" 


»,  -  tJ».  ,    (218) 


in  which  vl  is  to  be  calculated  from  the  temperature  7*,  and 
the  pressure  /,  by  aid  of  equation  (176)  or  (177),  while  vt  is 
to  be  found  from  the  equation 


The  value  of  *,  for  the  final  condition  can  be  determined 
by  aid  of  equation  (185), 

^-  +  0,  +,,  log,  |j  =  *£  +  *,. 

4"i  *••»•,*« 

Finally,  the  weight  discharged  per  second  may  be  found 
by  the  equation 

aV 

w  =  —  . 
». 

In  this  work  the  most  expeditious  way  is  to  make  numer- 
ical calculations  by  the  several  equations  without  attempting 
any  further  algebraic  reduction.  The  pressure  in  the  orifice 
will  be  very  nearly  0.6  of  the  pressure  /,  in  the  reservoir, 
provided  that  /,  is  more  than  f  the  pressure  of  the  atmosphere 
into  which  discharge  takes  place. 


1 62          THERMODYNAMICS   OF  THE  STEAM-ENGINE, 

EXAMPLES. 

1.  Find  the  velocity  of  flow  of  air  from  the  pressure  of 
6  atmospheres  in  a  reservoir  to  the  pressure  of  5  atmospheres 
in  the  throat  of  the  orifice;  also  from   5   to  4  atmospheres, 
from  4  to  3,  and  from  3  to  2,  the  inicial  temperature  in  each 
case  being  30°  C.     Ans.    175. r,,  193.9,    219.2,  258.0   metres 
per  sec. 

2.  Find   the  weight  of  air  per  second  that  will  be   dis- 
charged from  an  orifice   '  inch  in  diameter,  from  a  reservoir 
having  the  temperature  ( 3°  F.  and  a  pressure  of  150  pounds 
per  square  inch,  into  t1  j  atmosphere.       Ans.   2.736  Ibs. 

3.  Find  the  weight  of    saturated  steam  per  second   dis- 
charged through  an  orifice   I  inch  in  diameter,  from  a  boiler 
having  the  gauge-pressure  60  pounds,  into  the  atmosphere. 
Find  also  for  the  following  values  of  x,  0.9,  0.8,  0.6,  0.5, 
0.4,  0.2,  and  for  hot  water.     Ans.   0.850  Ibs.;  0.893,  0.943, 
1.077,  1-169,  1-289,  1.710,3.064. 

4.  Find  the  velocity  of  flow  of  superheated  steam  with 
the  initial  temperature  360°  F.  and  initial  pressure  100  pounds 
absolute,  when  the  pressure  in  the  throat  of  the  orifice  is  60 
pounds  absolute.      Ans.    1400  ft.  per  sec. 

5.  In  example  4  find  the  weight  per  second  discharged 
through  an  orifice  i  inch  in  diameter.     Ans.    1.09  Ibs. 


CHAPTER    IX. 
INJECTOR^. 


• 


AN  injector  is  an  instrument  by  means  of  which  a  jet  of 
steam  acting  on  a  stream  of  water  witT^  which  it  mingles,  and 
by  which  it  is  condensed,  can  impart  to  the  resultant  jet  of 
water  a  sufficient  velocity  to  overcome  a  pressure  that  may 
be  equal  to  or  greater  than  the  initial  pressure  of  the  steam. 
Thus,  steam  from  a  boiler  may  force  feed-water  into  the  same 
boiler,  or  into  a  boiler  having  a  higher  pressure.  The 
mechanical  energy  of  the  jet  of  water  is  derived  from  the  heat 
energy  yielded  by  the  condensation  of  the  steam-jet.  There 
is  no  reason  why  an  injector  cannot  be  made  to  work  with  any 
volatile  liquid  and  its  vapor,  if  occasion  may  arise  for  doing 
so;  but  in  practice  it  is  used  only  for  forcing  water.  An 
essential  feature  in  the  action  of  an  injector  is  the  condensa- 
tion of  the  steam  by  the  water  forced ;  other  instruments  using 
jets  without  condensation,  like  the  water-injector  in  which  a 
small  stream  at  high  velocity  forces  a  large  stream  with  a  low 
velocity,  differ  essentially  from  the  steam-injector. 

Method  of  Working. — A  very  simple  form  of  injector  is 
shown  by  Fig.  31,  consisting  of  three  essential  parts,  a  the 
steam-nozzle,  b  the  combining- tube  ^  and  c  the  delivery-tube. 
Steam  is  supplied  to  the  injector  through  a  pipe  connected 
at  d\  water  is  supplied  through  a  pipe  at  /,  and  the  injector 
forces  water  out  through  the  pipe  at  e.  The  steam-pipe  must 
have  on  it  a  valve  for  starting  and  regulating  the  injector,  and 
the  delivery-pipe  leading  to  the  boiler  must  have  on  it  a 

163 


r 

OF   TKK 


164 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


check-valve  to  prevent  water  from  the  boiler  from  flowing 
back  through  the  injector  when  it  is  not  working.  The 
water-supply  pipe  commonly  has  a  valve  for  regulating  the 
flow  of  water  into  the  injector. 

This  injector,  known  as  a  non-lifting  injector,  has  the 
water-reservoir  set  high  enough  so  that  water  will  flow  into 
the  injector  through  the  influence  of  gravity.  A  lifting 


FIG.  31. 

injector  has  a  special  device  for  making  a  vacuum  to  draw 
water  from  a  reservoir  below  the  injector,  which  will  be 
described  later. 

To  start  the  injector  shown  by  Fig.  31,  the  steam-valve  is 
first  opened  slightly  to  blow  out  any  water  that  may  have 
gathered  above  the  valve,  through  the  overflow,  since  it  is 
essential  to  have  dry  steam  for  starting.  The  steam-valve  is 
then  closed,  and  the  water-valve  is  opened  wide.  As  soon 
as  water  appears  at  the  overflow  between  the  combining-tube 
and  the  delivery-tube  the  steam-valve  is  opened  wide,  and  the 
jet  of  steam  from  the  steam-nozzle  mingles  with  and  is  con- 
densed by  the  water  and  imparts  to  it  a  high  velocity,  so  that 
it  passes  across  the  overflow  space  between  the  combining- 
tube  and  the  delivery-tube  and  passes  into  the  boiler.  When 
the  injector  is  working  a  vacuum  is  formed  at  the  space 


INJECTORS.  165 

between  the  combining  and  delivery  tubes,  and  the  valve  at 
the  overflow  then  closes  and  excludes  air  which  would  mingle 
with  the  water  and  might  interfere  with  the  action  of  the 
injector. 

Theory  of  the  Injector. — The  two  fundamental  equa- 
tions of  the  theory  of  the  injector  are  deduced  from  the  prin- 
ciples of  the  conservation  of  energy  and  the  conservation  of 
momenta. 

The  heat  energy  in  one  pound  of  steam  at  the  absolute 
pressure  pl  in  the  steam-pipe  is 


where  rl  and  ^,  are  the  heat  of  vaporization  and  heat  of  the 

liquid  corresponding  to  the  pressure  p^ ;  -j-  is  the  mechanical 

./i 

equivalent  of  heat  (778  foot-pounds),  and  x^  is  the  quality  of 
the  steam;  if  there  is  two  per  cent  of  moisture  in  the  steam, 
then  ;r,  is  0.98. 

Suppose  that  the  water  entering  the  injector  has  the  tem- 
perature /„  and  that  its  velocity  where  it  mingles  with  the 
steam  is  VJ ;  then  its  heat  energy  per  pound  is 


and  its  kinetic  energy  is 


where  q*  is  the  heat  of  the  liquid  at  /„  and  g  is  the  accelera- 
tion due  to  gravity  (32.2  feet). 

If  the  water  forced  by  the  injector  has  the  temperature  ttt 


166          THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

and  if  the  velocity  of  the  water  in  the  smallest  section  of  the 
delivery-tube  is  FTO,  then  the  heat  energy  per  pound  is 


and  the  kinetic  energy  is 


Let  each  pound  of  steam  draw  into  the  injector  y  pounds 
of  water;  then,  since  the  steam  is  condensed  and  forced 
through  the  delivery-tube  with  the  water,  there  will  be  i  -f-  y 
pounds  delivered  for  each  pound  of  steam.  Equating  the  sum 
of  the  heat  and  kinetic  energies  of  the  entering  steam  and 
water  to  the  sum  of  the  energies  in  the  water  forced  from  the 
injector,  we  have 


The  terms  depending  on  the  velocities  VJ  and  Vw  are 
never  large  and  can  commonly  be  neglected.  Thus,  for  a 
lifting-injector  the  pressure  causing  water  to  enter  the  injector 
is  always  less  than  the  pressure  of  the  atmosphere  and  for  a 
non-lifting  injector  it  is  only  a  little  more.  If  the  pressure 
of  the  atmosphere  is  14.7  pounds  per  square  inch  and  if  there 
is  a  perfect  vacuum  in  the  injector,  then  by  equation  (204), 
the  heat  equivalent  df  the  term  depending  on  Fw',  assuming 
y  to  be  15,  will  be 

y~i  =  15  X         X  I44d4.7  -  o)         =  0.6  B.T.  u, 


If  the  injector  delivers  v^ater  against  a  boiler-pressure  of 
150  pounds  by  the  gauge  or  164.7  pounds  absolute,  then  the 


INJECTORS.  167 

heat  equivalent  of  the  term  depending  on  Fw  will  be 

^F,'_i6x  144x164.7 

>-^F     778  x  62.4 

In  both  calculations  the  pressure  of  the  water-jet  in  the 
smallest  section  of  the  combining  tube  is  assumed  to  be  small 
enough  to  be  neglected.  The  determination  of  the  term 
depending  on  Vm  comes  from  the  consideration  that  Vv  must 
be  greater  than  the  velocity  with  which  cold  water  would  flow 
out  under  the  influence  of  the  boiler-pressure. 

Now  since  r1  is  always  greater  than  800,  the  term  depend- 
ing on  Fw  is  about  one  per  cent  of  the  total  left-hand  mem- 
ber of  equation  (219),  and  the  term  depending  on  Vwr  is  less 
than  one  tenth  of  a  per  cent.  For  practical  calculations  we 
may  neglect  both,  reducing  equation  (219)  to 


Equation  (220)  may  be  applied  to  any  kind  of  injector, 
including  double  injectors  which  have  two  steam-nozzles. 

For  example,  if  dry  steam  is  supplied  to  the  injector  at 
1  20  pounds  by  the  gauge  or  134.7  pounds  absolute,  if  the 
supply-temperature  of  the  water  is  65°  F.,  and  if  the  delivery- 
temperature  is  165°  F.,  then  the  water  pumped  per  pound  of 
steam  is 

^  +  01  —  ?4      867.4+  321.2  —  133.4 

'  =  -£=*-  =      .33.4-33."     "  ias  pounds- 

The  momentum  of  one  pound  of  steam  issuing  from  the 
steam-nozzle  with  the  velocity  Vs  is  V,  -4-  g\  the  momentum 
of  y  pounds  of  water  entering  the  combining-tube  with  the 
velocity  VJ  is  yVJ  -5-  g\  and  the  momentum  of  I  -\-  y  pounds 
of  water  at  the  smallest  section  of  the  delivery-tube  is 


1  68       THERMODYNAMICS  OF  THE  STEAM-ENGINE. 

(\  _|_  j/)  Vw  -±.  g.  Equating  the  sum  of  the  momenta  of 
water  and  steam  before  mingling  to  the  momentum  of  the 
combined  water  and  steam  in  the  delivery-tube, 


(221) 


This  equation  can  be  used  to  calculate  any  one  of  the 
velocities  provided  the  other  two  can  be  determined  inde- 
pendently. Unfortunately  there  is  much  uncertainty  about 
all  of  the  velocities  so  that  the  proper  sizes  of  the  orifices  and 
of  the  forms  and  proportions  of  the  several  members  of  an 
injector  have  been  determined  mainly  by  experiment.  The 
best  exposition  of  this  matter  is  given  by  Mr.  Strickland 
Kneass,*  who  has  made  many  experiments  for  Wm.  Sellers 
&  Co.  The  practical  part  of  what  follows  is  largely  drawn 
from  his  work. 

Velocity  of  the  Steam-jet.  —  Equation  (214)  gives 


where  rl  and  gl  are  the  heat  of  vaporization  and  the  heat  of 
the  liquid  of  the  supply  of  steam  at  the  pressure  plt  and  r^ 
and  <?,  are  corresponding  quantities  at  the  pressure/.,  for  that 
section  of  the  tube  for  which  the  velocity  is  calculated ;  xl  is 
the  quality  of  the  steam  at  the  pressure  pl  (usually  0.98  to 
unity)  and  x^  is  the  quality  at  the  pressure  /„  to  be  calculated 
by  aid  of  the  equation 


Here  7*,  and  7,  are  the  absolute  temperatures  corresponding 
to  the  pressures/,  and  /„,  and  #,  and  #9  are  the  entropies  of 

*  Practice  and  Theory  of  the  Injector,  J.  Wiley  &  Sons. 


INJECTORS.  169 

the  liquid  at  the  same  pressures.      Of  course  -r  is  the  me- 

si 

chanical  equivalent  of  heat  and  g  is  the  acceleration  due  to 
gravity. 

In  the  discussion  of  the  flow  of  steam  it  appeared  that  the 
pressure  in  an  orifice  with  rounded  approach  is  about  T6¥  of 
the  absolute  pressure  of  the  steam  in  the  pipe  leading  to  the 
orifice,  and  that  the  quantity  of  steam  discharged  is  not 
affected  by  the  pressure  against  which  the  discharge  takes 
place,  provided  the  latter  is  not  more  than  half  the  pressure 
causing  the  flow.  This  principle  may  be  applied  with  fair 
approximation  to  the  injector,  so  far  as  the  calculation  of  the 
amount  of  steam  used  by  an  injector  is  concerned;  conversely 
the  same  principle  can  be  used  for  calculating  the  size  of  the 
orifice  in  the  steam-nozzle.  If  preferred,  Rankine's  equation 
(page  158)  can  be  used  for  this  purpose.  But  it  is  pointed 
out  by  Mr.  Kneass  that  by  flaring  or  expanding  the  steam- 
nozzle  the  pressure  in  it  may  be  reduced,  and  consequently 
the  velocity  of  the  steam  discharged  may  be  very  much 
increased.  Experiments  on  a  nozzle  of  a  Sellers'  injector 
showed  that  the  pressure  at  the  exit  when  the  injector  was 
working  was  a  little  less  than  the  pressure  of  the  atmosphere 
for  various  pressures  from  60  to  120  pounds  by  the  gauge. 
Applying  to  a  special  case,  we  have, 

For  example,  the  velocity  of  discharge  from  a  straight 
orifice  under  the  pressure  of  1 20  pounds  by  the  gauge  or 
134.7  pounds  absolute  is 


=  {2X  32.2  X  778(867.4-  0.967  X  895.1  +  321.2  —  282.1)1* 
=  1430  feet  per  second, 
having  for  xt 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


=  0.9670, 

provided  that/a  =  o.6/,  =  80.8  pounds  absolute. 

If,    however,  the  pressure  at    the   exit  of  an   expanded 
nozzle  is  14.7  pounds  absolute,  then 

867.4  \ 

+  a5025  -  °'3I27  =  a8775' 


and 


F,  =  {2X  32.2x778(867.4  —  0.8711  X  965.8+321.2  —  180.8)}* 
=  2830  feet  per  second, 

which  is  nearly  twice  that  just  calculated  for  the  velocity  at 
the  smallest  section  of  the  steam-nozzle. 

Velocity  of  Entering  Water.  —  The  velocity  of  the  water 
in  the  combining-tube  where  it  mingles  with  the  steam 
depends  on  (a)  the  lift  or  head  from  the  reservoir  to  the 
injector,  (b)  the  pressure  (or  vacuum)  in  the  combining-tube, 
and  (c)  on  the  resistance  which  the  water  experiences  from 
friction  and  eddies  in  the  pipe,  valves,  and  passages  of  the 
injector.  The  first  of  these  can  be  measured  directly  for  any 
given  case  ;  for  example,  where  a  test  is  made  on  an  injector. 
In  determining  the  proportions  of  an  injector  it  is  safe  to 
assume  that  there  is  neither  lift  nor  head  for  a  non-lifting 
injector,  and  that  the  lift  for  a  lifting-injector  is  as  large  as 
can  be  obtained  with  certainty  in  practice.  The  lift  for  an 
injector  is  usually  moderate,  and  seldom  if  ever  exceeds 
20  feet. 

The  vacuum  in  the  combining-tube  may  amount  to  22  or 
24  inches  of  mercury,  corresponding  to  25  or  27  feet  of  water; 
that  is,  the  absolute  pressure  may  be  3  or  4  pounds  per  square 


INJECTORS.  171 

inch.  The  vacuum  after  the  steam  and  water  are  combined 
appears  to  be  limited  by  the  temperature  of  the  water; 
thus,  if  the  temperature  is  165°  F.,  the  absolute  pressure 
cannot  be  less  than  5.3  pounds.  But  the  final  temperature 
is  taken  in  the  delivery-pipe  after  the  water  and  condensed 
steam  are  well  mixed  and  are  moving  with  a  moderate 
velocity. 

The  resistance  of  friction  in  the  pipes,  valves,  and  passages 
of  injectors  has  never  been  determined;  since  the  velocity  is 
high  the  resistance  must  be  considerable. 

If  we  assume  the  greatest  vacuum  to  correspond  to  27  feet 
of  water,  the  maximum  velocity  of  the  water  entering  the 
combining-tube  will  not  exceed 


P 


=  V2  X  32.2  X  27  =  42  feet. 

If,  on  the  contrary,  the  effective  head  producing  velocity 
is  as  small  as  5  feet,  the  corresponding  velocity  will  be 


V2  X  32.2  X  5  =  1  8  feet. 

It  cannot  be  far  from  the  truth  to  assume  that  the  velocity 
of  the  water  entering  the  combining-tube  is  between  20  and 
40  feet  per  second. 

Velocity  in  the  Delivery-tube.  —  The  velocity  of  the 
water  in  the  smallest  section  of  the  delivery-tube  may  be 
estimated  in  two  ways:  in  the  first  place  it  must  be  greater 
than  the  velocity  of  cold  water  flowing  out  under  the  pressure 
in  the  boiler,  and  in  the  second  place  it  may  be  calculated  by 
aid  of  equation  (221),  provided  that  the  velocities  of  the 
entering  steam  and  water  are  determined  or  assumed. 

For  example,  let  it  be  assumed  that  the  pressure  of  the 
steam  in  the  boiler  is  120  pounds  by  the  gauge,  and  that, 
as  calculated  on  page  167,  each  pound  of  steam  delivers  10.5 
pounds  of  water  from  the  reservoir  to  the  boiler.  As  there 
is  a  good  vacuum  in  the  injector  we  may  assume  that  the 


I/2          THERMODYNAMICS   OF   THE   STEAM-ENGINR. 

pressure  to  be  overcome  is  132  pounds  per  square  inch,  corre- 
sponding to  a  head  of 


Now  the  velocity  of  water  flowing  under  the  head  of  305 
feet  is 


V2gh  =  V2  X  32.2  X  305  =  140  feet  per  second. 

The  velocity  of  steam  flowing  from  a  pressure  of  120 
pounds  by  the  gauge  through  a  diverging-tube  with  the  pres- 
sure equal  to  that  of  the  atmosphere  at  the  exit  has  been 
calculated  to  be  2830  feet  per  second.  Assuming  the  velocity 
of  the  water  entering  the  combining-tube  to  be  20  feet,  then 
by  equation  (221)  we  have  in  this  case 


If  the  steam  is  assumed  to  flow  through  a  converging- 
nozzle  then  the  velocity  at  120  pounds  boiler-pressure  will 
be  1430  feet  per  second,  and  the  velocity  of  the  water-jet 
becomes 

.430  +  10.5  X  20  = 

I   +  10.5 

Since  there  is  considerable  resistance  due  to  friction  and 
to  sudden  change  of  velocity  in  leaving  the  delivery-tube,  this 
last  velocity  is  probably  insufficient.  But  if  the  entrance 
velocity  is  assumed  to  be  30  feet,  then  the  calculation  gives 
151  feet  for  the  velocity  in  the  delivery-tube,  which  is  prob- 
ably enough  to  make  the  injector  work. 

Sizes  of  the  Orifices.  —  From  direct  experiments  on  in- 
jectors it  appears  that  the  quantity  of  steam  delivered  by  the 
steam-nozzle  can  be  calculated  in  all  cases  by  the  method  for 


INJECTORS.  173 

the  flow  of  steam  through  a  straight  orifice,  assuming  the 
pressure  in  the  orifice  to  be  -£$  of  the  absolute  pressure  above 
the  orifice. 

Now  each  pound  of  steam  forces  y  pounds  of  water  from 
the  reservoir  to  the  boiler;  consequently  if  w  pounds  are 
drawn  from  the  reservoir  per  second  the  injector  will  use 
w  -*-  y  pounds  of  steam  per  second. 

The  specific  volume  of  the  mixture  of  water  and  steam  in 
the  smallest  section  of  the  steam-nozzle  is 


where  x^  is  the  quality,  u,  is  the  increase  of  volume  due  to 
vaporization,  and  cr  is  the  specific  volume  of  the  water.  The 
volume  of  steam  discharged  per  second  is 


y  ' 

and  the  area  of  the  orifice  is 

(223) 


where  Vs  is  the  velocity  at  the  smallest  section. 

For  example,  for  a  flow  from  134.7  pounds  absolute  to 
80.8  pounds  absolute  x^  is  0.9670  and  Vs  is  1430  feet,  as 
found  on  page  169.  Again,  for  an  increase  of  temperature 
from  65°  F.  to  165°  F.  the  water  per  pound  of  steam  is  10.5. 
Calculating  the  specific  volume  at  80.8  pounds,  we  have 

v^  =  .*,«,+  <r  =  0.9670(5.375—  o.o  1  6)+  o.o  1  6  =  5.198  cubic  feet. 

If  the  injector  is  required  to  deliver  1200  gallons  an  hour, 
or 

1200  X  231  X62.4  ^ 
1728  X6o  X6o 


1/4  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

pounds  per  second,  the  area  of  the  steam-nozzle  must  be 
wv^       2.78  X  5.198 


-  -      -  —  - 

yV.        10.5  X  H30 


=  0.000962  square  feet. 


The  corresponding  diameter  is  0.420  of  an  inch,  or  10.6  mil- 
limetres. 

In  trying  to  determine  the  size  of  the  orifice  in  the 
delivery-tube  we  meet  with  two  serious  difficulties:  we  do  not 
know  the  velocity  of  the  steam  in  the  smallest  section  of  the 
delivery-tube,  and  we  do  not  know  the  condition  of  the  fluid 
at  that  place.  It  has  been  assumed  that  the  steam  is  entirely 
condensed  by  the  water  in  the  combining-tube  before  reach- 
ing the  delivery-tube,  but  usually  there  are  small  bubbles  of 
uncondensed  steam  still  mingled  with  the  water,  so  that  the 
actual  density  of  the  heterogeneous  mixture  is  from  0.6  to 
0.9  that  of  water.  Since  the  pressure  at  the  entrance  to  the 
delivery-tube  is  small,  the  specific  volume  of  the  steam  is  very 
large,  and  a  fraction  of  a  per  cent  of  steam  is  enough  to  reduce 
the  density  of  the  steam  to  one-half.  Even  if  the  steam  is 
entirely  condensed,  the  air  carried  b'y  the  water  from  the 
reservoir  is  enough  to  sensibly  reduce  the  density  at  the  low 
pressure  (or  vacuum)  found  at  the  entrance  to  the  delivery- 
tube. 

If  Vw  is  the  probable  velocity  of  the  jet  at  the  smallest 
section  of  the  delivery-tube,  and  if  6  is  the  density  of  the 
fluid,  then  the  area  of  the  orifice  in  square  feet  is 


for  each  pound  of  steam  mingles  with  and  is  condensed  byjj/ 
pounds  of  water  and  passes  with  that  water  through  the 
delivery-tube;  ze/,  as  before,  is  the  number  of  pounds  of  water 
drawn  from  the  reservoir  per  second. 

For  example,  let  it  be  assumed  that  the  actual  velocity  in 


INJECTORS.  175 

the  delivery-tube  to  overcome  a  boiler-pressure  of  120  pounds 
by  the  gauge  is  150  feet  per  second,  and  that  the  density  of 
the  jet  is  about  0.9  that  of  water;  then  with  the  value  of 
w  =  2.78  and  y  =  10.5,  we  have 

w(i  +y)  2.78  X  11.5 

*-  =  ~VJhT  -  150X0.9X62.4X7^?  =  ''^i  sq.  ft. 

The  corresponding  diameter  is  0.257  °f  an  inch,  or  6.5  mil- 
limetres. 

Steam-nozzle. — The  entrance  to  the  steam-nozzle  should 
be  well  rounded  to  avoid  eddies  or  reduction  of  pressure  as 
the  steam  approaches;  in  some  injectors,  as  the  Sellers' 
injector,  Fig.  32,  the  valve  controlling  the  steam  supply  is 
placed  near  the  entrance  to  the  nozzle,  but  the  bevelled 
valve-seat  will  not  interfere  with  the  flow  when  the  valve 
is  open. 

It  has  already  been  pointed  out  that  the  steam-nozzle  may 
advantageously  be  made  to  expand  or  flare  from  the  smallest 
section  to  the  exit.  The  length  from  that  section  to  the  end 
may  be  between  two  and  three  times  the  diameter  at  that 
section. 

Consider  the  case  of  a  steam-nozzle  supplied  with  steam 
at  1 20  pounds  boiler-pressure:  it  has  been  found  that  the 
velocity  at  the  smallest  section,  on  the  assumption  that  the 
pressure  is  then  80.8  pounds,  is  1430  feet  per  second,  and  that 
the  specific  volume  is  5.198  cubic  feet.  If  the  pressure  is 
reduced  to  14.7  pounds,  that  is,  to  atmospheric  pressure,  at 
the  exit,  the  velocity  becomes  2830  feet  per  second,  the 
quality  being  x^  =  0.8775.  The  specific  volume  is  conse- 
quently 

z/s  =  xji^  -\-  (T  =  0.8775(26.60  —  0.016)  +  0.016  =  23.34  cu.  ft. 

The  areas  will  be  directly  as  the  specific  volumes  and 
inversely  as  the  velocities,  so  that  for  this  case  we  shall  have 


I/O  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

the  ratio  of  the  areas 

5.198  :  23.34 
2830  :  1430 

and  the  ratio  of  the  diameters  will  be 

1/1     1/2.27  =  i  :  1.5. 

Combining-tube. — There  is  great  diversity  with  different 
injectors  in  the  form  and  proportions  of  the  combining-tube. 
It  is  always  made  in  the  form  of  a  hollow  converging 
cone,  straight  or  curved.  The  overflow  is  commonly  con- 
nected to  a  space  between  the  combining-tube  and  the 
delivery-tube;  it  is,  however,  sometimes  placed  beyond  the 
delivery-tube,  as  in  the  Sellers'  injector,  Fig.  32.  In  the 
latter  case  the  combining  and  delivery  tubes  may  form  one 
continuous  piece,  as  is  seen  in  the  double  injector  shown  by 

Fig.  33- 

The  Delivery-tube. — This  tube  should  be  gradually  en- 
larged from  its  smallest  diameter  to  the  exit  in  order  that  the 
water  in  it  may  gradually  lose  velocity  and  be  less  affected  by 
the  sudden  change  of  velocity  where  this  tube  connects  to  the 
pipe  leading  to  the  boiler. 

It  is  the  custom  to  rate  injectors  by  the  size  of  the 
delivery-tube;  thus  a  No.  6  injector  may  have  a  diameter  of 
6  mm.  at  the  smallest  section  of  the  delivery-tube. 

Mr.  Kneass  found  that  a  delivery-tube  cut  off  short  at  the 
smallest  section  would  deliver  water  against  35  pounds  pres- 
sure only,  without  overflowing;  the  steam-pressure  being  65 
pounds.  A  cylindrical  tube  four  times  as  long  as  the  internal 
diameter,  under  the  same  conditions  would  deliver  only 
against  24  pounds.  A  tube  with  a  rapid  flare  delivered 
against  62  pounds,  and  a  gradually  enlarged  tube  delivered 
against  93  pounds. 

If  the  delivery-tube  is  assumed  to  be   filled  with  water 


INJECTORS.  177 

without  any  admixture  of  steam  or  air,  then  the  relative 
velocities  at  different  sections  may  be  assumed  to  be  propor- 
tional to  the  corresponding  areas.  This  gives  a  method 
of  tracing  the  change  of  velocity  of  the  water  in  the  tube 
from  its  smallest  diameter  to  the  exit. 

A  sudden  change  in  the  velocity  is  very  undesirable,  as 
at  the  point  where  the  change  occurs  the  tube  is  worn  and 
roughened,  especially  if  there  are  solid  impurities  in  the  water. 
It  has  been  proposed  to  make  the  form  of  the  tube  such  that 
the  change  of  velocity  shall  be  uniform  until  the  pressure  has 
fallen  to  that  in  the  delivery-pipe;  but  this  idea  is  found  to  be 
impracticable,  as  it  leads  to  very  long  tubes  with  a  very  wide 
flare  at  the  end. 

Efficiency  of  the  Injector. — The  injector  is  used  for 
feeding  boilers,  and  for  little  else.  Since  the  heat  drawn  from 
the  boiler  is  returned  to  the  boiler  again,  save  the  very  small 
part  which  is  changed  into  mechanical  energy,  it  appears  as 
though  the  efficiency  was  perfect,  and  that  one  injector  is 
as  good  as  another  provided  that  it  works  with  certainty. 
We  may  almost  consider  the  injector  to  act  as  a  feed-water 
heater,  treating  the  pumping  in  of  feed-water  as  incidental. 
It  has  already  been  pointed  out  on  page  167  that  the  kinetic 
energy  of  the  jet  in  the  delivery-tube  is  less  than  one  per  cent 
of  the  energy  due  to  the  condensation  of  the  steam.  On  this 
account  the  injector  is  used  wherever  cold  water  must  be 
forced  into  a  boiler,  as  on  a  locomotive,  or  when  sea-water  is 
supplied  to  a  marine  boiler.  Considering  only  the  advantage 
of  supplying  hot  water  to  the  boiler,  it  almost  seems  as 
though  the  more  steam  an  injector  uses  the  better  it  is. 
Such  a  view  is  erroneous,  as  it  is  often  desirable  to  supply 
water  without  immediately  reducing  the  steam-pressure  and 
then  it  is  necessary  to  use  as  little  steam  as  may  be.  It  is, 
however,  true  that  simplicity  of  construction  and  certainty  of 
action  are  of  the  first  importance  in  injectors. 

Lifting  Injector. — The  injector  described  at  the  begin- 


1/8 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


ing  of  this  chapter  was  placed  so  that  water  from  the  reservoir 
would   run   in   under  the   influence    of  gravity.     When    the 


injector  is  placed  higher  than  the  reservoir  a  special  device  is 
provided  for  lifting  the  water  to  start  the  injector.  Thus  in 
the  Sellers'  injector,  Fig.  32,  there  is  a  long  tube  which  pro- 


INJECTORS  179 

trudes  well  into  the  combining-tube  when  the  valves  w  and  x 
are  both  closed.  When  the  rod  B  is  drawn  back  a  little  by 
aid  of  the  lever  H  the  valve  w  is  opened,  admitting  steam 
through  a  side  orifice  to  the  tube  mentioned.  Steam  from 
this  tube  drives  out  the  air  in  the  injector  through  the  over- 
flow, and  water  flows  up  into  the  vacuum  thus  formed,  and  is 
itself  forced  out  at  the  overflow.  The  starting-lever  H  is  then 
drawn  as  far  back  as  it  will  go,  opening  the  valve  x  and  sup- 
plying steam  to  the  steam-nozzle.  This  steam  mingles  with 
and  is  condensed  by  the  water  and  imparts  to  the  water 
sufficient  velocity  to  overcome  the  boiler-pressure.  Just  as 
the  lever  H  reaches  its  extreme  position  it  closes  the  overflow 
valve  K  through  the  rod  L  and  the  crank  at  R. 

Since  lifting-injectors  may  be  supplied  with  water  un^pr 
a  head,  and  since  a  non-lifting  injector  when  started  will  lift 
water  from  a  reservoir  below  it,  or  may  even  start  with  a 
small  lift,  the  distinction  between  them  is  not  fundamental. 

Double  Injectors. — The  double  injector  illustrated  by 
Fig.  33,  which  represents  the  Korting  injector,  consists  of 
two  complete  injectors,  one  of  which  draws  water  from  the 
reservoir  and  delivers  it  to  the  second,  which  in  turn  delivers 
the  water  to  the  boiler.  To  start  this  injector  the  handle  A 
is  drawn  back  to  the  position  B  and  opens  the  valve  supply- 
ing steam  to  the  lifting-injector.  The  proper  sequence  in 
opening  the  valves  is  secured  by  the  simple  device  of  using  a 
loose  lev^kfor  joining  both  to  the  valve-spindle;  for  under 
steam-pressure  the  smaller  will  open  first,  and  when  it  is  open 
the  larger  will  move.  The  steam-nozzle  of  the  lifter  has  a 
good  deal  of  flare,  which  tends  to  form  a  good  vacuum.  The 
lifter  first  delivers  water  out  at  the  overflow  with  the  starting- 
lever  at  M\  then  that  i^w  is  pulled  as  far  as  it  will  go,  open- 
ing the  valve  for  the  second  injector  or  forcer,  and  closing 
both  overflow  valves. 

Automatic  Injectors. — In  the  discussions  of  injectors 
thus  far  given  it  has  been  assumed  that  they  work  at  full 
capacity,  but  as  an  injector,  must  be  able  to  bring  the  water- 


i8o 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


level  in  a  boiler  up  promptly  to  the  proper  height,  it  will 
have  much  more  than  the  capacity  needed  for  feeding  the 
boiler  steadily.  Any  injector  may  be  made  to  work  at  a 
reduced  capacity  by  simply  reducing  the  opening  of  the 
steam-valve,  but  the  limit  of  its  action  is  soon  reached.  The 


FIG.  33. 

limit  may  be  extended  somewhat  by  partially  closing  the 
water-supply  valve  and  so  limiting  the  water- supply. 

The  original  Giffard  injector  had  a  movable  steam-nozzle 
to  control  the  thickness  of  the  sheet  of  water  mingling  with 
the  steam,  and  also  had  a  long  conical  valve  thrust  into  the 
steam-nozzle  by  which  the  effective  area  of  the  steam-jet 
could  be  regulated.  Thus  both  water  and  steam  passages 
could  be  controlled  without  changing  the  pressures  under 
which  they  were  supplied,  and  the  injector  could  be  regulated 
to  work  through  a  wide  range  of  pressures  and  capacities. 
The  main  objection  was  that  the  injector  was  regulated  by 
hand  and  required  almost  constant  attention. 

In  the  Sellers  injector,  Fig.  32,  the  regulation  of  the 
steam-supply  by  a  long  cone  thrust  through  the  steam-nozzle 
is  retained,  but  the  supply  of  water  is  regulated  by  a  movable 


INJECTORS.  l8l 

combining-tube,  which  is  guided  at  each  end  and  is  free  to 
move  forwards  and  backwards.  At  the  rear  the  combining- 
tube  is  affected  by  the  pressure  of  the  entering  water,  and  in 
front  it  is  subjected  to  the  pressure  in  the  closed  space  O, 
which  is  in  communication  with  the  overflow  space  between 
the  combining-tube  and  the  delivery-tube,  in  this  injector  the 
space  is  only  for  producing  the  regulation  of  the  water-supply 
by  the  motion  of  the  combining-tube,  as  the  actual  overflow 
is  beyond  the  delivery-tube  at  K.  When  the  injector  is 
running  at  any  regular  rate  the  pressures  on  the  front  and  the 
rear  of  the  combining-tube  are  nearly  equal,  and  it  remains  at 
rest.  If  the  supply  of  steam  is  decreased  by  partially  closing 
the  steam-valve  or  by  reducing  the  boiler-pressure,  the 
velocity  of  the  water  in  the  combining-tube  is  diminished  and 
the  pressure  in  the  chamber  O  increased,  so  that  the  combin- 
ing-tube is  forced  back  and  the  supply  of  water  is  regulated 
to  correspond  with  the  steam-supply.  A  contrary  action 
ensues  if  the  supply  of  steam  is  increased  either  by  raising  the 
boiler-pressure  or  by  opening  the  steam-valve  wider.  The 
injector  is  always  started  at  full  capacity  by  pulling  the  steam- 
valve  wide  open,  as  already  described;  after  it  is  started  the 
steam-supply  is  regulated  at  will  by  the  engineer  or  boiler 
attendant,  and  the  water  is  automatically  adjusted  by  the 
movable  combining-tube,  and  the  injector  will  require  atten- 
tion only  when  a  change  of  the  rate  of  feeding  the  boiler  is 
required  on  account  of  either  a  change  in  the  draught  of  steam 
from  the  boiler,  or  a  change  of  steam-pressure,  for  the 
capacity  of  the  injector  increases  with  a  rise  of  pressure. 

The  action  of  this  injector  is  well  represented  by  the  fol- 
lowing table  of  experimental  results,  furnished  by  the  makers: 

For  each  pressure  of  steam  noted  in  column  I,  the  water 
was  delivered  by  the  injector  into  the  boiler  under  approxi- 
mately the  same  pressure.  The  delivery  was  measured  by 
observing  the  indications  of  a  water-meter.  The  pressures  in 
column  8  were  obtained  by  throttling  the  steam  supplied  to 
the  injector,  and  observing  the  pressure  at  which  it  ceased  to 


182 


THERMOD  YNAMICS   OF   THE   STEAM-ENGINE. 


EXPERIMENTS  ON  A  SELLERS  INJECTOR. 
(Diam.  Water-orifice  6  mm.) 


T3  «  ^     • 

S3 

S  3"°  j2 

DELIVERY 

TEMPERATURE, 

£J 

•-Ja 

liu* 

in  Cubic  Feet  per  Hour. 

Fahrenheit  Degrees. 

g-|M. 

sfc. 

Ipt 

2b 
11 

Delivered  Water. 

j|| 

ll 

f  3  5' 

II 

6 

g 

^_  u  G 

11 

W-lS-O 

a 

£ 

aj 

| 

it 

ft 

gl| 

^o«" 

3^.S  S 

1 

7 

s 

°-~ 

\t 

8  a 

'c.> 

3-0  M 

4>  ^  fcuo 

{•K 

1 

73 

i 

P 

£ 

1s 

?Q 

I21 

|15 

i 

2 

3 

4 

5 

6 

7 

8 

9 

10 

75-3 

63.6 

0.845 

66 

IOO 

94 

3 

132 

20 

82.4 

61.2 

0-743 

66 

108 

104 

9 

i34 

30 

94-2 

56.5 

0.600 

66 

114 

116 

16 

i34 

40 

100.  I 

60.0 

0-599 

66 

I2O 

123 

22 

132 

5° 

108.3 

64-7 

o-597 

66 

I24 

125 

27 

131 

60 

116.5 

63.6 

0.546 

66 

127 

133 

34 

130 

70 

124.8 

63.6 

0.510 

67 

I30 

142 

40 

130 

80 

133.0 

67.1 

0-505 

66 

134 

144 

46 

131 

90 

141-3 

69-5 

0.492 

67 

I36 

148 

S2 

T32 

100 

147.2 

64.7 

0.456 

66 

•  140 

T59 

58 

132 

no 

J53-o 

67.1 

0-439 

67 

I44 

162 

63 

132 

120 

156.6 

73-o 

0.466 

67 

I48 

162 

69 

134 

I30 

161.2 

74-2 

0.460 

66 

ISO 

165 

75 

130 

140 

166.0 

78.9 

.0.476 

66 

153 

1  66 

81 

126 

150 

170.7 

70.6 

0.414 

66 

I57 

167 

88 

121 

work,  each  experiment  being  repeated  several  times  with  pre- 
cisely the  same  results.  The  temperatures  in  column  9  were 
obtained  by  gradually  heating  the  water  supplied  to  the 
injector,  and  noting  the  temperature  at  which  it  ceased  to 
operate,  each  temperature  recorded  being  checked  by  several 
repetitions  of  the  experiment. 

A  double  injector,  such  as  that  represented  by  Fig.  33,  is 
to  a  certain  extent  automatic,  since  an  increase  of  steam- 
pressure  causes  at  once  an  increase  in  the  amount  of  water 
drawn  in  by  the  lifter  and  an  increase  in  the  flow  of  steam 
through  the  steam-nozzle  of  the  forcer.  Such  injectors  have 
a  wide  range  of  action  and  can  be  controlled  by  regulating 
the  valve  on  the  steam-pipe. 


INJECTORS. 


183 


Restarting  Injectors. — If  the  action  of  any  of  the  injec- 
tors thus  far  described  is  interrupted  for  any  reason,  it  is 
necessary  to  shut  off  steam  and  start  the  injector  anew; 
sometimes  the  injector  has  become  heated  while  its  action  is 
interrupted,  and  there  may  be  difficulty  in  starting.  To 
overcome  this  difficulty  various  STEAM 

forms  of  restarting  injectors  have 
been  devised,  such  as  the  Gresham 
represented  by  Fig.  34.  This  in- 
jector has  four  jets  arranged  in  line, 
as  follows:  the  steam-nozzle,  the 
draught-tube,  the  movable  ccin- 
bining-tube,  and  the  delivery-tube. 
When  the  injector  is  not  working 
the  movable  combining-tube  rests 
on  the  upper  end  of  the  tube  in 
which  it  slides,  and  leaves  a  free 
passage  to  the  overflow.  When 
steam  is  admitted  through  the 
steam-nozzle  it  expels  the  air  in 
the  injector,  draws  in  water  from 
the  reservoir  and  throws  -it  out  at 
the  overflow.  As  soon  as  the  supply  of  water  is  established 
so  that  it  can  condense  the  steam,  sufficient  velocity  is  im- 
parted to  cause  the  water  to  pass  through  the  delivery-tube,, 
and  a  vacuum  is  produced  above  the  combining-tube  which 
draws  it  up  and  shuts  off  the  passage  to  the  overflow.  If  the 
action  of  the  injector  is  temporarily  interrupted  the  combin- 
ing-tube drops  down  and  the  instrument  is  ready  to  start  as 
soon  as  water  is  supplied  to  it. 

Sellers'  self-acting  injector,  represented  by  Fig.  35,  is 
both  an  automatic  and  a  restarting  injector.  It  is  a  double 
injector  with  all  the  jets  in  one  line;  #,  b,  and  c  are  the 
steam-nozzle,  the  combining-tube,  and  the  delivery-tube  of 
the  forcer;  the  lifter  is  composed  of  the  annular  steam-nozzle 
d,  and  the  annular  delivery-tube  e,  surrounding  the  nozzle  a* 


1 84          THERMODYNAMICS   Of    THE   STEAM-ENGINE. 


INJECTORS.  185 

The  proportions  are  such  that  the  lifter  can  always  produce  a 
suction  in  the  feed-pipe  even  when  there  is  a  discharge  from 
the  main  steam-nozzle,  and  it  is  this  fact  that  establishes  the 
restarting  feature.  When  the  feed-water  rises  to  the  tubes  it 
meets  the  steam  from  the  lifter-nozzle  and  is  forced  in  a  thin 
sheet  and  with  high  velocity  into  the  combining-tube  of  the 
forcer,  where  it  comes  in  contact  with  the  main  steam-jet, 
and  mingling  with  and  condensing  it,  receives  a  high  velocity 
which  enables  it  to  pass  the  overflow  orifices  and  proceed 
through  the  delivery-tube  to  the  boiler. 

Like  any  double  injector,  the  lifter  and  forcer  have  a  con- 
siderable range  of  action  through  which  the  water  is  adjusted 
to  the  steam-supply;  but  there  is  a  further  adjustment  in  this 
injector,  for  when  a  good  vacuum  is  established  in  the  space 
surrounding  the  combining-tube,  water  can  enter  through  the 
check-valve/,  and  flowing  through  the  orifices  in  the  combin- 
ing-tube mingles  with  the  jet  in  it,  and  is  forced  with  that  jet 
into  the  boiler. 

The  steam-valve  is  seated  on  the  end  of  the  lifter-nozzle, 
and  it  has  a  protruding  plug  which  enters  the  forcer-nozzle. 
When  the  valve  is  opened  to  start  the  injector,  steam  is  sup- 
plied first  to  the  starter,  and  soon  after,  by  withdrawing  the 
plug,  to  the  forcer.  If  the  steam  is  dry  the  starting-lever 
may  be  moved  back  promptly ;  if  there  is  condensed  water  in 
the  steam-pipe,  the  starting-handle  should  be  moved  a  little 
way  to  first  open  the  valve  of  the  lifter,  and  then  it  is  drawn 
as  far  back  as  it  will  go,  as  soon  as  water  appears  at  the  over- 
flow. The  water-supply  may  be  regulated  by  the  valve  g, 
which  can  be  rotated  a  part  of  a  turn.  The  minimum  delivery 
of  the  injector  is  obtained  by  closing  this  valve  till  puffs  of 
steam  appear  at  the  overflow,  and  then  opening  it  enough 
to  stop  the  escape  of  steam. 

When  supplied  with  cold  water  this  injector  wastes  very 
little  in  starting.  If  the  injector  is  hot  or  is  filled  with  hot 
water  when  started,  it  will  waste  hot  water  till  the  injector  is 
cooled  by  the  water  from  the  feed-supply,  and  will  then  work 


1 86          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

as  usual.  If  air  leaks  into  the  suction-pipe  or  if  there  is  any 
other  interference  with  the  normal  action,  the  injector  wastes 
water  or  steam  till  normal  conditions  are  restored,  when  it 
starts  automatically. 

The  following  table  gives  the  results  of  tests  made  on  an 
injector  of  this  type:* 

TEST   OF   A    SELLERS    IMPROVED    INJECTOR   OF    1887,  SIZE  10$, 
LIFT  4  FEET,  SUPPLY-WATER    WEIGHED. 

MAXIMUM    CAPACITY. 


Mean  steam-pressure  

30 

60 

122 

151 

200.5 

I. 

Gallons  of  water  per  hour  

1912 

2535 

3517 

3765 

4005 

2. 

Temperature  of  supply-water... 

67.0 

67.0 

54-o 

50.0 

50-5 

3- 

Temp,  of  delivered  water  

113.25 

I25.O 

J33-4 

135-7 

154.0 

4- 

Weight    of    water     delivered  \ 
per  pound  of  steam  used.  .  .  } 

25.90 

IQ.IO 

13.60 

1  2.  60 

10.34 

MINIMUM 

CAPACITY. 

Mean  steam-pressure  

30 

60 

120 

148 

200.6 

5- 

Gallons  of  water  per  hour  

765 

937 

I29O 

1432 

1732 

6. 

Temperature  of  supply-water... 

67.0 

67.0 

54-5 

55-0 

50.0 

7- 

Temp,  of  delivered  water  

171 

212 

238 

250 

263 

RANGE. 

Mean  steam-pressure  

30 

60 

121 

149-5 

200.5 

8. 

Per  cent  min.  capacity  of  max.. 

40.0 

37-0 

36.6 

38.0 

43.2 

9- 

Actual  range  in  gals,  per  hr  .  .. 

1147 

1598 

2227 

2333 

2273 

10. 

Percent  range  of  max.  capacity. 

6o.O 

63.0 

63-3 

62.0 

56.8 

LIMITING    TEMPERATURE    OF 

WATER-SUPPLY. 

Mean  steam-pressure  

30 

60 

1  2O 

150 

II. 

Limiting  re-starting  temp  

130 

135 

122 

1  2O 

12. 

Limiting  operating  temp  

139 

144 

137 

133 

In  these  tests  the  amount  of  water  supplied  to  the  injector 
was  measured;  the  amount  of  water  delivered  per  pound  of 
steam  was  calculated  by  aid  of  equation  (220). 

Exhaust-steam  Injectors. — Injectors  supplied  with  ex- 
haust-steam from  a  non-condensing  engine  can  be  used  to 
feed  boilers  up  to  a  pressure  of  about  80  pounds.  Above 
this  pressure  a  supplemental  jet  of  steam  from  the  boiler  must 

*  The  Railroad  Gazette,  Dec.  n,  1896. 


INJECTORS. 


187 


be  used.  Such  an  injector,  as  made  by  Schaffer  and  Buden- 
berg,  is  represented  by  Fig.  36;  when 
used  with  low  boiler-pressure  this  in- 
jector has  a  solid  cone  or  spindle  in- 
stead of  the  live-steam  nozzle.  To 
provide  a  very  free  overflow  the  com- 
bining-tube  is  divided,  and  one  side  is 
hung  on  a  hinge  and  can  open  to  give 
free  exit  to  the  overflow  when  the 
injector  is  started.  When  the  injector 
is  working  it  closes  down  into  place. 
The  calculation  for  an  exhaust-steam 
injector  shows  that  enough  velocity 
may  be  imparted  to  the  water  in  the 
delivery-tube  to  overcome  a  moderate 
boiler-pressure. 

For  example \  an  injector  supplied  with  steam  at  atmos- 
pheric pressure,  and  raising  the  feed-water  from  40°  F.  to 
1 00°  F.,  will  draw  from  the  reservoir 


FIG.  36. 


1146.6  —  68.01 
68.01  —  8.06 


—  1 8.0 


pounds  of  water  per  pound  of  steam.  Adiabatic  expansion 
to  the  pressure  of  7.8  pounds  will  reduce  the  steam  to  the 
quality 


•*•  = 


642.7/965. 


;.8  \ 

—  +  0.3127  -  0.2667]  =  0.9649. 


986.9^672. 
The  velocity  of  the  steam  will  be 
[/  =  52x32X778(1146.6-0.9649X986.9—150.6)^=1480  feet. 

Assuming  the  water  to  enter  the  combining-tube  with  a 
velocity  of  30  feet,  the  velocity  of  the  jet  in  the  delivery-tube 
will  be 


1 88          THERMODYNAMICS  OF   THE  STEAM-ENGINE. 
and  it  can  overcome  a  pressure  of 

To62  X  62.4 

=  75.6  pounds  absolute. 

2  X  32.2  X  144 

Tests  of  Injectors. — The  table  opposite  gives  the  results 
of  tests  made  on  several  different  injectors  by  Messrs.  Bradlee 
and  Blanchard,*  in  the  laboratories  of  the  Massachusetts 
Institute  of  Technology: 

Sizes  of  Orifices. 

Hancock:  lifter,  steam 0.114 

"  forcer,  steam 0.206 

"  "  water 0.149 

Lombard:  steam 0.224 

"  water 0.164 

Dodge:  steam o  161 

"  water 0.131 

The  experiments  15  to  21,  inclusive,  were  made  with  im- 
proved methods  of  reducing  the  evaporation  of  the  hot  water 
delivered  by  the  injector,  and  the  results  are  more  consistent 
and  reliable  than  the  preceding  ones.  It  is  apparent  that  the 
weight  of  steam  used,  which  is  obtained  by  taking  the  differ- 
ence between  the  weights  of  water  supplied  and  delivered,  is 
diminished  by  the  evaporation,  and  that  consequently  the 
experimental  quantity  of  water  delivered  by  one  pound  of 
steam  is  made  too  large  thereby :  this  explains  part  of  the 
discrepancy  of  the  first  fourteen  experiments. 

The  calculation  for  Experiment  17  on  the  Dodge  injec- 
tor, on  the  assumption  that  the  pressure  in  the  steam-orifice 
is  0.6  of  the  absolute  boiler-pressure,  and  the  steam  in  the 
supply-pipe  contains  three  per  cent  of  moisture,  gives  for  the 
quality  in  the  orifice  0.94,  for  the  velocity  of  the  steam-jet 

*  Thesis,  1888. 


INJECTORS. 


I89 


;u3D  jad 


2S222222S 


ATK 
nd  o 


•1U30J 

-uadxg  Xg 


o     o     M     moo     o 


•spanoj 

3d  pasn  ureais 


•spanoj 
'anoH 

J3Q  p9J9AIpp  JSIB^Y 


M      O 

00        M 


•spunoj 
'jnou 
aad  patiddn 


PERATURE 
hrenheit. 


?  & 


£  £  £  tf  £  8  £  #:::::::  5  S  <S 


jo  saqoui  ut  oolong 


qouj  -bg  jad  spnnoj 


GAUGE  PRESS 
ounds  per  Sq. 


•JO]3aCaj  jo  a 


190 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


1398  feet,  and  for  the  specific  volume  in  the  orifice  7.76  cubic 
feet.  The  discharge  through  the  steam-nozzle  by  calculation 
is  91.7  pounds,  while  the  experiment  showed  93.1  pounds; 
which  is  fairly  satisfactory,  as  the  steam  is  determined  by 
taking  the  difference  between  the  water  supplied  to  and  that 
delivered  by  the  injector.  If  the  velocity  of  the  water  enter- 
ing the  combining-tube  is  assumed  to  be  20  feet,  then  the 
velocity  of  the  jet  in  the  delivery-tube  appears  to  be  144  feet, 
while  the  velocity  required  to  overcome  the  delivery-pressure 
of  74  pounds  by  the  gauge  or  88.7  pounds  absolute  is  115 
feet.  But  if  the  jet  is  assumed  to  be  clear  water  with  a 
density  of  62.4  pounds,  the  velocity  calculated  from  the  area 
of  the  steam-orifice  and  the  quantity  of  water  delivered  wil! 
be  78  feet  per  second;  consequently  the  density  of  the  jet 
will  be  about  0.60  that  of  water. 

Water-injector. — Fig.    37   represents   a   device   called   a 
water-injector,  in  which  a  small  stream  of  water  in  the  pipe 


FIG.  37. 

M  flowing  from  the  reservoir  R  raises  water  from  the  reservoir 
R"  to  the  reservoir  R' . 

Let  one  pound  of  water  from  the  reservoir  R  draw  y 
pounds  from  R" ,  and  deliver  I  +  y  pounds  to  R'.  Let  the 
velocity  of  the  water  issuing  from  A  be  v\  that  of  the  water 


INJECTORS.  191 

entering  from  R"  be  v9  at  N\  and  that  of  the  water  in  the 
pipe  O  be  zv     The  equality  of  momenta  gives 

......     (225) 


Let  x  be  the  excess  of  pressure  at  M  above  that  at  N 
expressed  in  feet  of  water;  then 


v?  =  2gx ; (226) 

-J   =2g(H-\-x)\ (227) 

V?   =   2g(h+*) (228) 

Substituting  in  equation  (225), 


VH+x-Vh  +  x 

-~   •  •  •  •  (229) 


It  is  evident  from  inspection  of  the  equation  (229)  that  y 
may  be  increased  by  increasing  x ,  for  example,  by  placing 
the  injector  above  the  level  of  the  reservoir  so  that  there  may 
be  a  vacuum  in  front  of  the  orifice  A. 

If  the  weight  G  of  water  is  to  be  lifted  per  second,  then 

-  pounds  per  second  must  pass  the  orifice  A,  G  pounds  the 

space  at  N,  and  \i-\--jG  pounds  through  the  section  at  O\ 

which,  with  the  several  velocities^,  v^  and  vlt  give  the  data 
for  the  calculation  of  the  required  areas. 

PROBLEM. — Required  the  calculation  for  a  water-injector 
to  raise  1200  gallons  of  water  an  hour,  H  =  96  ft.,  h  =  12  ft., 

x  =  4  ft. 

—  V  100  =  10;    Vh  -fx  =  Vl6  =  4  ; 
10  —  4 


THERMOD  YNAMICS   OF   7 "HE   STEAM-ENGINE, 

The  velocities  are 


v  —  V2  x  32.2  X  ioo  =  80.25  feet  per  second  ; 
vl  —  1/2  X  32.2  X  16  =  32.10  feet  per  second; 


z/a  =  1/2  X  32.2  X  4     =  16.05  feet  Per  second. 

1  200  gallons  an  hour  =  0.04452  cubic  feet  per  second. 
The  areas  are 

0.04452 
a  ~'=  3  x  80.25       =  aoooi85  scluare  feet  ; 

4  X  0.04452 

a.  =  -  -  =  0.06185  square  feet; 

3  X  32.10 

0.044  5  2 
#,  =      ^  =  0.00277  square  feet. 

The  diameters  corresponding  to  the  velocities  v  and  vl  are 

d  =  o.i  8  of  an  inch  ; 
dl  —  0.58  of  an  inch. 

The  area  a^  is  of  annular  form,  having  the  area  0.4  of  a 
square  inch. 

Ejector.  —  When  the  injector  is  used  for  raising  water 
where  there  is  no  advantage  in  heating  the  water,  it  is  a  very 
wasteful  instrument.  The  efficiency  is  much  improved  by 

arranging  the  instrument  as  in 
Fig.  38,  so  that  the  steam-nozzle 
_  A  shall  deliver  a  small  stream  of 
water  at  a  high  velocity,  which, 
as  in  the  water-injector,  delivers 

a  larger  stream  at  a  less  velocity.  Each  additional  conical 
nozzle  increases  the  quantity  at  the  expense  of  the  velocity, 
so  that  a  large  quantity  of  water  may  be  lifted  a  small  height. 
Ejectors  are  commonly  fitted  in  steamships  as  auxiliary 
pumps  in  case  of  leakage,  a  service  for  which  they  are  well 


INJECTORS.  1 93 

fitted,  since  they  are  compact,  cheap,  and  powerful,  and  are 
used  only  in  emergency,  when  economy  is  of  small  conse- 
quence. 

Ejector-condensers. — When  there  is  a  good  supply  of 
cold  condensing  water,  an  exhaust-steam  injector,  using  all 
the  steam  from  the  engine,  may  be  arranged  to  take  the  place 
of  the  air-pump  of  a  jet-condensing  engine.  The  energy  of 
the  exhaust-steam  flowing  from  the  cylinder  of  the  engine  to 
the  combining-tube,  where  the  absolute  pressure  is  less  and 
where  the  steam  is  condensed,  is  sufficient  to  eject  the  water 
and  the  air  mingled  with  it  against  the  pressure  of  the  atmos- 
phere, and  thus  to  maintain  the  vacuum. 

For  example,  if  the  absolute  pressure  in  the  exhaust-pipe 
is  4  pounds,  and  if  the  temperatures  of  the  injector  and  the 
delivery  are  60°  F.  and  100°  F.,  then  the  velocity  of  the 
steam-jet  will  be  1226  feet,  and  each  pound  of  steam  will 
draw  into  the  injector  24  pounds  of  water.  If  the  injection 
water  enters  with  a  velocity  of  20  feet,  the  velocity  of  tke 
water-jet  will  be  68.2  feet  per  second,  which  can  overcome 
the  pressure  of  3 1  pounds  absolute. 


CHAPTER    X 
HOT-AIR   ENGINES   AND   GAS-ENGINES. 

Engines  of  Maximum  Efficiency. — In  order  to  have  the 
maximum  efficiency,  an  engine  must  work  on  such  a  cycle 
that  its  working  substance  shall  always  have  the  temperature 
of  the  source  of  heat  when  acquiring  heat,  and  the  tempera- 
ture of  the  refrigerator  when  rejecting  heat;  that  is,  the 
engine  must  be  reversible. 

The  older  forms  of  hot-air  engines  all  had  the  source  of 
heat  at  one  constant  temperature  and  the  refrigerator  at 
another  lower  constant  temperature.  To  have  the  maximum 
efficiency  it  was  required  that  the  working  substance  should 
receive  heat  from  external  sources  at  one  temperature,  and 
reject  heat  to  external  spurces  at  one  temperature  only. 

Carnot's  engine  is  the  only  simple  engine  which  can  fulfil 
these  conditions  when  air  is  the  working  substance.  The 
cycle  of  that  engine  has  never  been  adopted  in  practice,  since 
it  involves  incompatible  requirements;  that  is,  the  isothermal 
changes  should  be  very  slow  and  the  adiabatic  changes  should 
be  very  rapid,  to  make  the  cycle  of  an  actual  engine  approxi- 
mate to  the  ideal  cycle.  And,  further,  Carnot's  cycle  for  a 
perfect  gas  is  so  attenuated  from  the  fact  that  the  angle 
between  an  isothermal  and  an  adiabatic  where  they  cross  is 
very  acute,  that  the  mean  effective  pressure  is  small,  and  the 
cylinder  of  the  engine  to  work  on  such  a  cycle  would  be  very 
large  for  the  power  developed. 

By  aid  of  a  device  called  a  regenerator  or  economizer, 
actual  engines  have  been  made  which  have  an  ideal  cycle  of 
maximum  efficiency.  Such  a  cycle  is  represented  by  Fig.  39. 

194 


HOT-AIR   ENGINES  AND    GAS-ENGINES.  1 95 

The  curves  DC  and  AB  are  isothermals,  which  form  those 
parts  of  the  cycle  during  which  heat  is  re-    IP 
ceived  from  the  source  and   rejected  to  the 
refrigerator.      The   curves  BC  and  DA   cor- 
respond to  the  adiabatic  lines  of  Carnot's 
cycle,  and  must  fulfil  the  condition  that  the 
heat  given   to  the   regenerator  during  one 


operation,  as  that  represented  by  BC,  must  FlG-  39- 

be  equal  to  the  heat  received  from  the  regenerator  during  the 

converse  operation  DA. 

To  obtain  the  relation  between  the  curves  BC  and  DA, 
draw  the  intermediate  isothermals  XZ  and  WY  with  a  differ- 
ence of  temperature  dt.  The  heat  received  by  one  unit  of 
weight  of  the  working  substance  in  passing  from  W  to  X  is 

dQ  =  cpdt  +  mdp<    .....     (230) 
.and  that  rejected  from  Z  to  Y  is 

dQ  =  cpdt  +  m'dp' (231) 

The  required  condition  will  be  fulfilled  by  making  equa- 
tion (230)  equal  to  equation  (231),  so  that 

mdp  =  m'dp' . 
Substituting  for  m  from  equation  (53)  gives 


Deducing  the  values  of  the  partial  differential  coefficients 
from  the  characteristic  equation  for  a  gas,  and  substituting, 
we  have 

R  J        R  , 
-dp  =  ^dp'; 

dp      dp 


(232) 


196 


THERMOD  YNAM1CS   OF   THE   STEAM-ENGINE. 


That  is,  the  required  relation  is  that  the  ratio  of  the  pressures 
at  the  points  cut  by  any  isothermal  from  the  paths  DA  and 
BC  must  be  constant. 

Stirling's  Engine. — This  engine  was  invented  in  1816, 
and  was  used  with  good  economy  for  a  few  years,  and  then 
rejected  because  the  heaters,  which  took  the  place  of  the 
boiler  of  a  steam-engine,  burned  out  rapidly.  It  is  described 
and  its  performance  given  in  detail  by  Ran- 
kine  in  his  Steam-engine.  An  ideal  sketch  is 
given  by  Fig.  40.  £  is  a  displacer  piston 
filled  with  non-conducting  material,  and  work- 
ing freely  in  an  inner  cylinder.  Between 
this  cylinder  and  an  outer  one  from  A  to  C 
is  placed  a  regenerator  made  of  plates  of 
metal,  wire  screens,  or  other  material,  so 
arranged  that  it  will  readily  take  heat  from 
or  yield  heat  to  air  passing  through  it.  At 


FIG.  40. 


the  lower  end  both  cylinders  have  a  hemispherical  head ;  that 
of  the  outer  cylinder  is  exposed  to  the  fire  of  the  furnace,  and 
that  of  the  inner  is  pierced  with  holes  through  which  the  air 
streams  when  displaced  by  the  plunger.  At  the  upper  end 
there  is  a  coil  of  pipe  through  which  cold  water  flows.  The 
working  cylinder  H  has  free  communication  with  the  upper 
end  of  the  displacer  cylinder,  and  consequently  it  can  be  oiled 
and  the  piston  may  be  packed  in  the  usual  manner,  since  only 
cool  air  enters  it. 

In  the  actual  engine  the  cylinder  H  is  double-acting,  and 
there  are  two  displacer  cylinders,  one  for  each  end  of  the 
working  cylinder. 

If  we  neglect  the  action  of  the  air  in  the  clearance  of  the 
cylinder  H  and  the  communicating  pipe,  we  have  the  follow- 
ing ideal  cycle.  Suppose  the  working  piston  to  be  at  the 
beginning  of  the  forward  stroke,  and  the  displacer  piston  at 
the  bottom  of  its  cylinder,  so  that  we  may  assume  that  the 
air  is  all  in  the  upper  part  of  that  cylinder  or  in  the  refriger- 
ator, and  at  the  lowest  temperature  7",,  the  condition  of  one 


HOT-AIR  ENGINES  AND    GAS-ENGINES.  1 97 

pound  of  air  being  represented  by  the  point  D  of  Fig.  39. 
The  displacer  piston  is  then  moved  quickly  by  a  cam  to  the 
upper  end  of  the  stroke;  while  the  working  P 
piston  moves  so  little  that  it  may  be  con- 
sidered to  be  at  rest.  The  air  is  thus  all 
driven  from  the  upper  end  of  the  displacer 
cylinder  through  the  regenerator,  from 
which  it  takes  up  heat  abandoned  during 


the  preceding  return  stroke,  thereby  acquir-  FlG<  4i- 

ing  the  temperature  T19  and  enters  the  lower  end  of  that 
cylinder.  During  this  process  the  line  AD  of  constant 
volume  is  described  on  Fig.  41.  When  this  process  is  com- 
plete, the  working  cylinder  makes  the  forward  stroke,  and  the 
air  expands  at  constant  temperature,  this  part  of  the  cycle 
being  represented  by  the  isothermal  AB  of  Fig.  41.  At  the 
end  of  the  forward  stroke  the  displacer  piston  is  quickly 
moved  down,  thereby  driving  the  air  through  the  regenerator, 
during  which  process  heat  is  given  up  by  the  air,  into  the 
upper  part  of  the  displacer  cylinder;  this  is  accompanied  by 
a  cooling  at  constant  volume,  represented  by  the  line  BC. 
The  working  piston  then  makes  the  return  stroke,  compress- 
ing the  air  at  constant  temperature,  as  represented  by  the 
isothermal  line  CD,  and  completing  the  cycle. 

To  construct  the  diagram  drawn  by  an  indicator,  we  may 
assume  that  in  the  clearance  of  the  cylinder  //",  the  communi- 
cating pipe,  and  refrigerator  there  is  a  volume  of  air  which 
flows  back  and  forth  and  changes  pressure,  but  remains  at  the 
temperature  7,.  If  we  choose,  we  may  also  make  allowance 
for  a  similar  volume  which  remains  in  the  waste  spaces  at  the 
lower  end  of  the  displacer  cylinder,  at  a  constant  tempera- 
ture T,. 

In  Fig.  42,  let  A  BCD  represent  the  cycle  of  operations-, 
without  any  allowance  for  clearance  or  waste  spaces;  the 
minimum  volume  will  be  that  displaced  by  the  displacer 
piston,  while  the  maximum  volume  is  larger  by  the  volume 
displaced  by  the  working  piston.  Let  the  point  E  represent 


IQ  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

the  maximum  pressure,  the  same  as  that  at  A  ;  and  the  united 
volumes  of  the  clearance  at  one  end  of  the  working  cylinder, 
of  the  communicating  pipe,  of  the  clearance  at  the  top  and 

bottom  of  the  displacer  cylinder,  and 
the  volume  in  the  refrigerator  and 
regenerator.  Each  part  of  this  com- 
bined volume  will  have  a  constant 
temperature,  so  that  the  volume  at 
different  pressures  will  be  represented 
by  the  hyperbola  EF.  To  find  the 
FIG-  42'  actual  diagram  A'B'C'D',  draw  any 

horizontal  line,  as  sy,  cutting  the  true  diagram  at  u  and  v, 
and  the  hyperbola  EF  at  /;  make  ux  and  vy  equal  to  st;  then 
x  and  y  are  points  of  the  actual  diagram.  The  indicator  will 
draw  an  oval  similar  to  A'B'C'D'  with  the  corners  rounded. 

To  show  that  the  diagram,  Fig.  41,  fulfils  the  condition 
for  maximum   efficiency,   drawn  an    intermediate  isothermal 
Since  DA  and  BC  are  lines  of  constant  volume, 


The  diagram  in  Fig.  43  was  reduced  from  an  indicator- 
diagram  from  a  recent  hot-air  engine  made  on  the  same  prin- 
ciple as  Stirling's  hot-air  engine.     To  avoid  destruction  of  the 
lubricant  in  the  working  cylinder 
Stirling  found  it  advisable  to  con- 
nect only  the  cool  end  of  the  dis- 
placer   cylinder  with  the  working 
cylinder,    and    had    two    displacer  - 
cylinders  for  one  working  cylinder. 

It  has  been  found  that  a  good  mineral  oil  can  be  used  to 
lubricate  the  displacer  piston,  and  that  the  hot  end  also  of  the 
displacer  cylinder  can  be  advantageously  connected  with  the 


HOT- AIR  ENGINES  AND    GAS-ENGINES.  199 

working  cylinders,  of  which  there  are  two.  Thus  each  work- 
ing cylinder  is  connected  with  the  hot  end  of  one  displacer 
cylinder  and  with  the  cool  end  of  the  other  displacer  cylinder. 

The  distortion  of  the  diagram  Fig.  43  is  due  in  part  to  the 
large  clearance  and  waste  space,  and  partly  to  the  fact  that 
the  displacer  pistons  are  moved  by  a  crank  at  about  70°  with 
the  working  crank. 

A  test  on  the  engine  mentioned  by  Messrs.  Underhill 
and  Johnson  *  showed  a  consumption  of  1.66  of  a  pound  of 
anthracite  coal  per  horse-power  per  hour;  but  the  friction  of 
the  engine  is  large,  so  that  the  consumption  per  brake  horse- 
power is  2.37  pounds.  This  engine,  like  the  original  Stirling 
engine  appears  to  have  given  much  difficulty  from  the  burn- 
ing of  the  heaters.  The  difficulty  is  likely  to  be  more  serious 
with  large  than  with  small  engines,  as  the  volume  of  the  dis- 
placer cylinders  increases  more  rapidly  than  the  heating 
surface. 

Ericsson's  Engine. — This  engine  consists  essentially  of  a 
working  cylinder,  a  compressing-pump,  and  a  reservoir.      To 
give  a  perfect  ideal  cycle,  a  regenerator  and  a  refrigerator  are 
required.      The  pump,  which  must  have  a  water-jacket  which 
acts  as  a  refrigerator,  draws  air  from  the  atmosphere  at  con- 
stant pressure,  compresses  it  at  constant    ip 
temperature,  and  forces  it  into  the  reser- 
voir under  constant  pressure.      The  pump 
cycle  is  represented  by  the  diagram  EDAF 
(Fig.   44).      The    engine   draws   air   from   ; 
the    reservoir  through    the    regenerator, 
during  which  process  it  is  heated    from 

the  temperature  71,  to  J1,;  the  supply  is  then  cut  off  by  a 
slide-valve,  and  the  air  in  the  cylinder  expands  at  constant 
temperature  down  to  the  atmospheric  pressure.  On  the 
return  stroke  the  air  is  forced  from  the  cylinder  at  constant 
pressure  through  the  regenerator,  being  thereby  cooled  to  the 

*  Thesis,  1889. 


F  I 


200  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

temperature  T^.  The  engine  cycle  is  represented  by  the 
diagram  FBCE.  The  diagram  of  effective  work  is  ABCD, 
which  fulfils  the  condition  of  maximum  efficiency,  since  AD 
and  BC  are  isothermals,  and  AB  and  CD  are  lines  of  constant 
pressure. 

The  actual  engine  does  not  expand  down  to  the  atmos- 
pheric pressure,  so  that  the  diagram  is  cut  short  by  a  line  like 
GH.  Also,  the  clearances  of  the  two  cylinders  introduce 
irregularities  and  modifications  of  the  diagram. 

An  engine  of  300  horse-power  designed  by  Ericsson  for  a 
ship  named  after  himself  used  about  2  pounds  of  coal  per 
indicated  horse-power  per  hour;  but  its  friction  was  exces- 
sive, and  it  was  finally  replaced  by  a  steam-engine.  Even 
when  this  type  of  engine  is  provided  with  a  regenerator  and 
is  made  to  work  on  a  closed  cycle  with  two  reservoirs,  one 
at  a  high  pressure  from  which  air  is  supplied  to  the  working 
cylinder,  and  one  at  a  lower  pressure  from  which  the  pump  is 
supplied,  it  may  be  expected  to  give  a  poorer  economy  than 
an  engine  working  on  the  Stirling  cycle. 

Gas-engines. — The  chief  difficulty  with  hot-air  engines  is 
to  transmit  heat  to  and  from  the  working  substance.  In  gas- 
engines  this  difficulty  is  removed  by  mixing  the  fuel  with  the 
air  (so  that  heat  is  developed  in  the  working  substance  itself), 
and  by  rejecting  the  hot  gases  after  they  have  done  their 
work.  The  fuel  may  be  illuminating-gas,  fuel-gas,  or  vapor 
of  a  volatile  liquid  like  gasoline.  It  will  be  shown  that  the 
specific  volume  and  the  specific  heat  of  the  mixture  of  air  and 
gas,  both  before  and  after  the  heat  is  developed  by  combus- 
tion, are  not  very  different  from  the  same  properties  of  air. 
The  general  theory  of  gas-engines  may  therefore  be  devel- 
oped on  the  assumption  that  the  working  substance  is  air, 
which  is  heated  and  cooled  in  such  a  manner  as  to  produce 
the  ideal  cycles  to  be  discussed,  as  is  done  by  Clerk.* 

Experience  has  shown  that  in  order  to  work  efficiently, 
the  mixture  of  gas  and  air  supplied  to  a  gas-engine  must  be 

*  Gas-tngines,  Dugald  Clerk. 


HOT-AIR   ENGIXES   AND    GAS-ENGINES.  2OI 

compressed  to  a  considerable  pressure  before  it  is  ignited. 
This  may  be  done  either  by  a  separate  compressor  or  in  the 
cylinder  of  the  engine  itself;  the  second  type  of  engines,  of 
which  the  Otto  engine  is  an  example,  is  the  only  successful 
type  at  the  present  time ;  the  other  type  has  some  advantages 
which  may  lead  to  its  development. 

Gas-engine  with  Separate  Compressor. — This  engine 
has  a  compressor,  a  reservoir,  and  a  working  cylinder.  When 
run  as  a  gas-engine  a  mixture  of  gas  and  air  is  drawn  into  a 
pump  or  compressor,  compressed  to  several  atmospheres,  and 
forced  into  a  receiver.  On  the  way  from  the  receiver  to  the 
working  cylinder  the  mixture  is  ignited  and  burned  so  that 
the  temperature  and  volume  are  much  increased.  After 
expansion  in  the  working  cylinder  the  spent  gases  are  ex- 
hausted at  atmospheric  pressure. 

The  ideal  diagram,  represented  by  Fig.  45,  has  a  general 
resemblance  to  that  of  Ericsson's  engine,  but  it  differs  essen- 
tially because  the  expansion  and  compression  curves  are 
adiabatics  instead  of  isothermal  lines.  ED  represents  the 
supply  of  the  combustible  mixture  to  the 
compressor,  DA  is  the  adiabatic  compres- 
sion, and  AF  represents  the  forcing  into 
the  receiver.  FB  represents  the  supply 
of  burning  gas  to  the  working  cylinder, 
BC  represents  the  expansion  and  CE  the 
exhaust.  In  practice  this  type  of  engine 

always  has  a  release,  represented  by  GH,  before  the  expan- 
sion has  reduced  the  pressure  of  the  working  substance  to 
that  of  the  atmosphere. 

This  type  of  engine  has  been  used  as  an  oil-engine  by 
supplying  the  fuel  in  the  form  of  a  film  of  oil  to  the  air  after 
it  has  been  compressed.  In  such  case  the  compressor  draws 
in  air  only,  and  there  is  not  an  explosive  mixture  in  the 
receiver.  The  Brayton  engine  when  run  in  this  way  could 
burn  crude  petroleum  or,  after  it  was  started,  could  burn 
refined  kerosene.  Its  chief  defect  appears  to  have  been  in- 


F  A 


V 


202  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

complete  combustion  and  consequent  fouling  of  the  cylinder 
with  carbon. 

The  effective  cycle  may  be  considered  to  be  represented 
by  the  diagram  ABCD  (Fig.  45),  and  may  be  assumed  to  be 
produced  in  one  cylinder  by  heating  the  air  from  A  to  B,  by 
cooling  it  from  C  to  D,  and  by  the  adiabatic  expansion  and 
compression  from  B  to  C  and  from  D  to  A.  If  Ta  and  Tb  are 
the  absolute  temperatures  corresponding  to  the  points  A  and 
By  then  the  heat  added  from  A  to  B  is 

ct(Tb-  Ta), 
and  the  heat  withdrawn  from  C  to  D  is 

cp(Tc  -  Td\ 
so  that  the  efficiency  of  the  ideal  cycle  is 


_.tTt)_         Te-Td 

cTb-T,  T-T- 


But  since  the  expansion  and  compression  are  adiabatic, 


but  pc  =  pd  and  pb  =  pa ,  therefore 
T        Ts  T  —  T 

•*•  c  •*•  d  1         •*•  c  *  * 


so  that  the  equation  for  efficiency  becomes 


HOT-AIR   ENGINES  AND    GAS-ENGINES.  203, 

For  example,    with   the    pressure   in    the   reservoir  at   90 
pounds  above  the  atmosphere  the  efficiency  is 


/  H.7  \    2'4°5 

7;  =  I  —    -  2-r  -  =  0.43. 

\  14.7  +  90' 

-;.- 

When  the  cycle  is  incomplete  the  expression  for  the 
efficiency  is  not  so  simple,  for  it  is  necessary  to  assume  cool- 
ing at  constant  volume  from  G  to  H  (Fig.  45),  and  cooling  at 
constant  pressure  from  //"to  D;  so  that  the  heat  rejected  is 

c,(Te-  Th)  +  cf(Tk-  Td), 
and  the  efficiency  becomes 

1(7;-  7-»)  +  (7i-  Tdy 

•7=1--         -~  --  7^         -•     •     •     (235) 

•*•  b  •*•  a 

. 

For  example,  let  it  be  assumed  that  the  pressure  at  A  is 
90  pounds  above  the  atmosphere,  that  the  temperature  at  B 
is  2500°  F.,  and  that  the  volume  at  G  is  three  times  the 
volume  at  B. 

First,  the  temperature  at  A  is 


provided  that  the  temperature  of  the  atmosphere  is  60°  F. 
The  temperature  at  G  is 


and  the  pressure  at  G  is 

(Vb\*  /jV-405 

A  =  P\-}  =  (H-7  +  9°)U      =  22-4  pounds, 


2O4  T  HER  MOD  YNAMICS    OF   THE   STEAM-ENGINE. 

so  that  the  temperature  at  H  is 


and  finally  the  efficiency  is 
i 


(1897  -  1247)  +  1247  -  520.7 


1.405 

77  =   I -E-2 ^ =  0.42. 

2960.7  —  917 

Gas-engine  with  Compression  in  Cylinder. — All  succes- 
ful  gas-engines  of  the  present  day  compress  the  explosive 
mixture  of  gas  and  air  in  the  working-cylinder,  and  as  they 
take  gas  at  one  end  of  the  cylinder  only  they  must  make  four 
strokes  for  each  explosion.  The  first  forward  stroke  of  the 
piston  from  the  head  of  the  cylinder  draws  in  the  mixture  of 
gas  and  air,  which  is  compressed  on  the  return  stroke;  at  the 
completion  of  this  return  stroke  the  mixture  is  ignited  and 
the  pressure  rises  very  rapidly;  the  next  forward  stroke  is  the 
working  stroke,  which  is  succeeded  by  an  exhaust  stroke  to 
expel  the  spent  gases.  In  almost  all  engines  these  four 
strokes  are  of  equal  length,  for  the  advantage  of  making  them 
of  unequal  length,  as  required  for  the  best  ideal  cycle,  is  more 
than  counterbalanced  by  the  mechanical  difficulty  of  produc- 
ing unequal  strokes. 

The  most  perfect  ideal  cycle,  represented  by  Fig.  46,  has 
four  strokes  of  unequal  length  so 
arranged  that  the  piston  starts  from 
the  head  of  the  cylinder  when  gas  is 
drawn  in,  and  the  pressure  in  the 
cylinder  is  reduced  to  that  of  the 
atmosphere  before  the  exhaust  stroke. 
Thus  there  is  the  filling  stroke,  rep- 
resented by  EC\  the  compression 
stroke,  represented  by  CD\  the  work- 
"  ing  stroke, represented  byAB\  and  the 

exhaust  stroke,  represented  by  BE. 
The  effective  cycle  is  ABCD,  which  may  be  considered  to 


P 


3ITY 


HOT-AIR   ENGINES  AND    GAS-ENGINES. 


be  performed  by  adding  heat  at  constant  volume  from  D  to 
A,  and  withdrawing  heat  at  constant  pressure  from  B  to  C, 
together  with  the  adiabatic  expansion  and  compression  AB 
and  CD. 

The  heat  added  under  this  assumption  is 

c,(Ta-  Td\ 
and  the  heat  rejected  is 

ct(Tb  -  Tc), 
so  that  the  efficiency  is 

_  cJjT.  -  T<)  -  cf(Tb  -Tf)_  Tt-Tc 

*=          c,(T.-Td)  *T.-T; 

If  the  temperature  at  A  and  the  pressure  at  D  are  assumed, 
then  it  is  necessary  to  make  preliminary  calculations  of  the 
temperatures  at  D  and  at  B  before  using  equation  (236)  by 
the  equations 


(237) 

(238) 

(239) 


For  example,  if  the  pressure  at  the  end  of  compression  is 
90  pounds  above  the  atmosphere,  and  the  temperature  at  the 
end  of  the  explosion  is  2500°  F.,  then 


Td  =  (60  +  460.7) 
provided  that  the  temperature  of  the  atmosphere  is  60°  F. 
/.  =  i04.7250°'t460-7  =  338  pounds; 


206  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


t?=  i  —  1.405 


1199-  520.7  _ 


2960.7-917 


=  0.55. 


If  the  expansion  is  not  carried  to  the 
atmospheric  pressure,  then  the  diagram 
shows  a  release  at  the  end  of  the  stroke, 
as  in  Fig.  47,  and  the  cycle  must  be  con- 
sidered to  be  formed  by  adding  heat  as 
before  at  constant  volume,  but  by  with- 
drawing heat  at  constant  volume  to  cause 
a  loss  of  pressure  from  B  to  G,  and  by 
withdrawing  heat  at  constant  pressure 
during  the  process  represented  by  GC. 


FIG.  47. 
The  heat  rejected  becomes,  therefore, 


and  the  efficiency  is 

_  cv(Ta  -  Td) 


cv(Tb  -  Tf)  -  cp(Tg  -  Tc) 


cv(Ta-Td) 
K(Tg-  T£) 


Ta  -  Td) 


(240) 


Assuming,  as  before,  the  pressure  at  D  and  the  tempera- 
ture at  A,  it  becomes  necessary  to  find  the  temperatures  at  B 
and  at  G  as  well  as  the  temperature  at  D\  this  last  may  of 
course  be  found  by  equation  (237).  If  the  pressure  at  B  is 
assumed  also,  then  equations  (238)  and  (239)  may  be  used  as 
before  to  find  Tb,  and  Tf  may  be  found  by  the  equation 


(240 


For  example,  let  it  be  assumed  that  the  expansion  ceases 
when  the  pressure  becomes  20  pounds  above  the  atmosphere, 


HOT-AIR  ENGINES  AND    GAS-ENGINES. 


207 


the    other   conditions    being    as   in    the    previous    example. 
Then 


=  1536; 


and 


i          I  536  -  650  +  I.405(6$0  -  520.7)  =  Q     o 

2960.7-917 


Though  not  essential  to  the  solution  of  the  example,  it  is 
interesting  to  know  that  the  volume  at  C  is 


/90+I47V  _ 
V      H7     ' 


times  the  volume  at  D,  and  that  the  volume  at  B  is 


times  the  volume  at  A. 

When,  as  in  common  practice,  the  four 
strokes  of  the  piston  are  of  equal  length 
the  diagram  takes  the  form  shown  by  Fig. 
48;  the  effective  cycle  may  be  considered 
to  be  equivalent  to  heating  at  constant 
volume  from  D  to  A  and  cooling  at  constant 
volume  from  B  to  C,  together  with  adiabatic 
expansion  and  compression  from  A  to  B  and 
from  C  to  D. 

The  heat  applied  is 

c,(Ta  -  Td), 
and  the  heat  rejected  is 

-  Tt\ 


FIG.  48. 


208  T  HER  MOD  YNAMICS    OF   THE   STEAM-ENGINE. 

so  that  the  efficiency  is 

_c,(T.-Td)-c,(Tt-Tc)_          Tt-Tc 

c,(T,-rd}  TT^T; 

Since  the  expansion  and  compression   are  adiabatic,   we 
have  by  equation  (79) 

Tbvf-*=Tava*-*,     and     7>tf«-'  =  7>/->; 

but  the  volumes  at  A  and  D  are  equal,  as  are  also  the  volumes 
at  B  and  C\  consequently  by  division 


consequently 

Tb-  Tc_  Tb       Te 
Ta-Td~  Ta~  Td 

and  the  expression  for  efficiency  becomes 


which  shows  that  the  efficiency  depends  only  on  the  compres- 
sion before  explosion. 

For  example,  if  the  volume  of  the  clearance  or  compres- 
sion space  is  one-third  of  the  piston  displacement,  so  that  vd 
is  one-fourth  of  vct  then  the  efficiency  is 

I\°405 

=0.43. 


The  pressure  at  the  end  of  compression  is 


1.405 
-)  =    I03.I 


HOT- AIR   ENGINES  AND    GAS-ENGINES.  2CX) 

pounds  absolute,  or  88.4  pounds  by  the  gauge.  The  calcu- 
lated efficiency  is  therefore  not  much  less  than  the  efficiencies 
found  for  other  examples;  it  is  notable  that  the  efficiency  is 
nearly  the  same  as  that  calculated  on  page  205  for  an  engine 
with  separate  compression  to  90  pounds  by  the  gauge.  For 
the  case  in  hand,  however,  the  pressure  after  explosion,  which 
depends  on  the  temperature,  may  exceed  300,  as  was  shown 
in  the  preceding  examples,  for  engines  with  compression  in 
the  cylinder. 

The  diagrams  from  engines  of  this  type  resemble  Fig.  49, 
which  was  taken  from  an  Otto  engine  tested  under  the  direc- 
tion of  Professor  Thurston.  Dur- 
ing the  filling  stroke  the  pressure  is 
gradually  reduced  below  that  of 
the  atmosphere;  the  explosion  is 
nearly  but  not  quite  instantaneous, 
as  is  shown  by  the  explosion  line  FlG-  49> 

leaning  toward  the  right  and  by  the  rounded  curve  joining  it 
to  the  expansion  line;  there  is  a  release  before  the  end  of  the 
stroke  and  a  little  back-pressure  at  the  beginning  of  exhaust. 
But  the  greatest  difference  between  this  diagram  and  the  ideal 
diagram  is  found  in  the  expansion  curve,  which  is  far  from 
being  an  adiabatic,  for  the  combustion  does  not  cease  when 
the  maximum  pressure  is  attained,  but  continues  throughout 
the  stroke;  and  at  the  same  time  heat  is  taken  up  energeti- 
cally by  the  walls  of  the  cylinder,  which  are  cooled  by  a  water- 
jacket  to  avoid  overheating.  These  two  effects,  after-burning 
and  loss  of  heat  to  the  water-jacket,  may  nearly  compensate, 
and  then  the  expansion  curve  will  resemble  the  adiabatic  line 
in  appearance. 

The  engine  from  which  this  diagram  was  taken  had  a 
diameter  of  8.5  inches  and  a  stroke  of  14  inches.  At  15$ 
revolutions  per  minute  it  indicated  9.6  horse-power  and 
developed  8.1  horse-power  on  a  brake.  It  consumed  24.5 
cubic  feet  of  illuminating-gas  per  horse-power  per  hour. 


210 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


Professor  Thurston  estimates  the  distribution  of  heat  as  fol' 

lows: 

Work  indicated  in  cylinder 17.0 

Heat  lost  to  cylinder  walls 52.0 

Heat  carried  away  by  exhaust  gases 15.5 

Heat  lost  by  conduction  and  radiation 15.5 


i  oo.o 
so  that  the  actual  efficiency  is  17  per  cent. 

The  compression  space  was  38  per  cent  of  the  total 
cylinder  volume,  so  that  the  efficiency  of  the  ideal  cycle  was 
42  per  cent,  and  the  ratio  of  the  efficiencies  was  about  0.40. 
More  modern  and  especially  larger  engines  use  less  gas  per 
horse-power  per  hour,  and  show  a  better  efficiency  both  abso- 
lutely and  relatively. 

There  are  two  questions  that  should  now  receive  consid- 
eration if  our  calculations  of  ideal  efficiency  are  to  be  taken 
as  a  guide  either  in  the  choice  of  a  type  of  engine  or  the  pro- 
portions of  a  type.  They  are  the  composition  of  the  mixture 
in  the  cylinder  both  before  and  after  explosion,  and  the  prob- 
able temperature  after  explosion.  As  for  the  composition  of 
the  mixture,  Clerk  gives  the  following  table  showing  the  com- 
position of  Manchester  illuminating-gas,  the  oxygen  required 
for  combustion,  and  the  volume  of  the  products  after  combus- 
tion, all  reduced  to  normal  pressure  and  temperature. 
ANALYSIS  OF  MANCHESTER  COAL-GAS.  (Bunsen  and  Roscoe.) 


Amount  required 
for  Complete 
Combustion. 

Products. 

vols. 

AC     C8 

vols.  O. 
22  7Q 

vols. 
4^  ^8    HoO 

Marsh-gas    CH\            

"34  Q 

69  8 

104  7      CO2  &  H2O 

Carbonic  oxide    CO    

6  64 

3  ao 

6  64    CO2 

Ethylene    C2H4        

4.O8 

12  24 

16  32    CO2  &  H2O 

Tetrvlene    C4H§ 

2  ^8 

14  28 

19  04    CO2  &  H2O 

Sulphuretted  hydrogen,  HaS. 
Nitrogen,  N  
Carbonic  acid,  CO2  

O.29 
2.46 
3-67 

0-43 

0.58,  H20&  SO2 
2.46 
3-67 

Total                    

IOO  OO 

122  86  O 

198  99  CO2  H2O&SOa 

HOT-AIR  ENGINES  AND    GAS-ENGINES.  211 

It  appears  in  this  case  that  the  volume  of  the  gas  and 
oxygen  is  reduced  by  combustion  from  223  to  199,  both  being 
at  freezing-point,  so  that  the  error  of  neglecting  such  a  change 
would  appear  to  be  about  10  per  cent.  But  the  gas  is  mixed 
with  from  7  to  12  volumes  of  air  when  it  is  introduced  into 
the  cylinder  of  the  engine  so  that  the  error  is  probably  less 
than  two  per  cent  in  any  case;  though  of  course  it  depends 
on  the  gas  used,  which  may  be  illuminating-gas  distilled  from 
coal,  so-called  water-gas,  or  crude  gas  made  in  a  special  gas- 
producer. 

To  find  the  most  economical  mixture  of  gas  and  air  and 
the  probable  temperature  after  combustion,  Clerk  made  a 
large  number  of  experiments  on  illuminating-gas  distilled 
from  coal.  He  found  the  pressure  immediately  after  explo- 
sion to  vary  from  40  to  90  pounds  per  square  inch  above  the 
atmosphere,  depending  on  the  kind  of  gas  and  the  proportions 
of  the  mixture.  Since  this  change  of  pressure  takes  place  at 
constant  volume  (neglecting  change  of  volume  due  to  combus- 
tion) the  absolute  temperatures  must  be  proportional  to  the 
absolute  pressures,  giving,  for  a  temperature  of  62°  F.  before 
explosion, 


.         (460.7  +  62)  =  1940, 

(460.7  +  62)i^±^=  3720, 

for  the  absolute  temperatures,  or  from  1500°  F.  to  3000°  F. 

The  temperature  after  explosion  appears  to  be  largely 
controlled  by  the  phenomenon  of  dissociation,  for  a  calculation 
of  the  temperature  of  combustion  on  the  assumption  that  the 
total  heat  of  combustion  of  the  gas  is  developed  during  the 
explosion  and  is  used  in  raising  the  temperature  of  the 
products  of  combustion  gives  temperatures  which  are  about 
double  those  just  stated.  When  the  temperature  of  the  gases 
after  explosion  has  been  reduced  by  expansion  and  by  con- 


12 


THERMODYNAMICS    OF    THE   STEAM-ENGINE. 


duction  and  radiation  to  the  cylinder  of  the  engine,  the  com- 
bustion may  be  continued  and  may  extend  throughout  the 
stroke;  this  phenomenon  is  called  after-burning. 

The  performance  of  gas-engines  has  been  improved  by 
(i)  raising  the  compression  before  explosion;  (2)  increasing 
the  size  of  the  engine;  (3)  clearing  the  cylinder  of  spent 
gases  before  introducing  a  new  charge  of  gas. 

The  following  table  of  tests  on  Crossley-Otto  engines  of 
about  the  same  size  illustrates  the  advantage  of  increasing  the 
compression : 


Q  O 

9e 

7  O 

Stroke 

18  o 

18  o 

T  C     O 

Ratio    of    compression  space  to   piston    dis- 
placement              .                     .... 

o  6 

OA 

Pressures  of  compression  above  atmosphere. 
Gas  per  horse-power  per  hour         

38.0 

2/1  o 

6l.6 

2O     ^ 

u.j4 

87.5 
14  8 

Actual  efficiency.  ...           .... 

O  17 

O  21 

OOC 

Theoretical  efficiency       .... 

O  ^7 

o  40 

o  428 

Or  T 

O  £7 

Or  Q 

^OJ 

Since  the  greatest  waste  of  the  gas-engine  is  due  to  the 
heat  carried  away  by  the  water-jacket,  it  is  to  be  expected 
that  a  large  engine  will  show  a  better  performance  than  a 
small  engine,  since  the  area  of  the  water-jacket  for  such  an 
engine  will  have  a  smaller  ratio  to  the  volume  of  the  cylinder. 
This  is  illustrated  by  the  following  results  from  engines  of 
different  sizes,  but  having  about  the  same  degree  of  compres- 
sion: 


Diameter  of  cylinder             .  . 

12    £> 

9c 

Stroke      

T  C 

21 

18 

OC 

Relative  capacity  
Actual  efficiency        

I 

O.  2C. 

3-77 

O  •  27^ 

i 

O    21 

2.97 

O277 

Theoretical  efficiency  

0.428 

o  .  428 

0.  40 

O    dl 

O   e.S 

Oe-7 

The  amount  of  heat  added  to  the  gases  during  explosion 
depends  to  a  large  extent  on  the  temperature  before  the 
explosion,  since  the  temperature  after  explosion  is  largely 
controlled  by  dissociation.  It  is  therefore  important  that  the 
engine  shall  be  charged  with  a  cool  mixture  of  air  and  gas. 


HOT-AIR   ENGINES  AND    GAS-ENGINES.  21$ 

But  the  compression,  or  cartridge  space,  as  it  is  sometimes 
called,  is  commonly  filled  with  hot  spent  gases  which  mingle 
with  and  raise  the  temperature  of  the  fresh  charge.  Three 
methods  of  meeting  this  difficulty  have  been  tried. 

1.  In  the  Clerk  engine  the  charge  of  gas  and  air  is  drawn 
into  an  auxiliary  cylinder  by  a  piston  driven  by  a  crank  which 
is  ninety  degrees  ahead  of  the  motor-crank.     The  charge  is 
lightly  compressed  and  is  forced  into  the  motor-cylinder  just 
before  the  motor-piston  reaches  the  end  of  the  stroke,  and 
drives  out  the  spent  gases  through  holes  in  the  walls  of  the 
cylinder  which  are  overrun  and  uncovered  by  the  piston  at 
the   proper   time.     The   return    stroke   of    the    motor-piston 
compresses  the  charge,  which  is  exploded  at  the  beginning  of 
the  next   forward  stroke.     This  engine  therefore   makes  an 
explosion  for  every  revolution.      In   practice  it  is  found  that 
the  fresh  charge  tends  to  mingle  with  the  spent  gases  and  that 
unburned  gas  escapes  in  the  exhaust,  so  that  there  is  little  if 
any  gain  in  efficiency  over  the  Otto  engine. 

2.  The  Atkinson  engine  has  a  double-beat  linkage  inter- 
posed between  the  piston  and  the  crank,  so  that  the  piston 
makes  four  strokes  of  unequal  length  for  each  revolution.    The 
diagram  from  the  Atkinson  engine  has  Fig.  47  for  its  ideal 
type.     In  the  first  place  the  piston  has  a  very  small  clearance 
at  the  end  of  the  exhaust  stroke  and  the  beginning  of  the 
filling  stroke;    and  also  the  expansion  reduces  the  pressure 
down   towards   that   of  the    atmosphere   before    release.      It 
appears  that  this  engine  showed  marked  improvement  over 
the  Otto  engines  with  which  it  was  compared,  but  the  com- 
plicated linkage  required  to  make  the  four  unequal  strokes 
gave  much  trouble,  especially  for  large  engines.     More  recent 
engines  of  the  Otto  type  have,  by  increased  size  and  compres- 
sion, given  better  economy  than  the  Atkinson  engines  which 
were  made  and  tested.     A  comparison  of  the  examples  on 
pages  207  and  208  shows  that  the  Otto  cycle  with  sufficient 
compression  may  be  expected  to  give  nearly  as  good  results 
as  an  engine  with  more  expansion. 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

3.  The  third  attempt  to  clear  the  cartridge  space  is  found 
in  the  Crossley  scavenging-engine,  in  which  advantage  is 
taken  of  the  fact  that  the  exhausts  from  the  cylinder  of  an 
Otto  engine  set  up  a  pulsation  in  the  exhaust-pipe,  and  that 
between  successive  exhausts  the  pressure  in  that  pipe  is  less 
than  the  pressure  of  the  atmosphere.  By  making  the  ex- 
haust-pipe of  the  right  length  (about  65  feet)  the  time  of  the 
reduced  pressure  between  the  pulsations  may  be  made  to 
coincide  with  the  completion  of  the  exhaust  stroke.  If  the 
inlet  air-valve  is  opened  at  this  time  fresh  air  sweeps  through 
the  cylinder  and  clears  it  of  spent  gases  before  the  next 
charge  of  gas  and  air  is  drawn  in.  Clerk  considers  that  a  gain 
of  five  per  cent  may  be  attained  by  properly  clearing  the 
cylinder  of  spent  gases ;  when  larger  gains  have  been  reported 
they  have  been  due  in  part  to  increased  compression  or  in- 
creased size. 

Gas-producers. — Illuminating  gas  must  be  refined  so  as 
to  remove  impurities  which  would  give  an  offensive  odor  when 
burning,  and  is  consequently  an  expensive  fuel,  and  can 
seldom  compete  on  even  terms  with  coal  burned  to  make 
steam.  Large  gas-engines  have  been  supplied  with  a  cheap 
gas  made  specially  for  them  by  distillation  and  partial  combus- 
tion of  coal  and  coke.  The  Dawson  gas-producer,  which  has 
been  successfully  used,  in  practice  has  a  closed  furnace  into 
which  anthracite  or  coke  is  charged  through  a  hopper  and 
charging-valve.  Air  is  forced  into  the  furnace  under  a  slight 
pressure  by  a  steam-jet  from  a  special  small  steam-boiler. 
The  fire  is  kept  about  18  inches  thick  to  give  incomplete 
combustion,  and  gives  off  a  gas  which  in  a  certain  instance  had 
the  composition: 

Dowson  Gas.  Ideal  Gas. 

Nitrogen 48.98  45.0 

Carbon  monoxide 25.07  39.0 

Hydrogen 18.73  i°-o 

Marsh-gas 0.31 

Olefiant  gas 0.31 

Carbon  dioxide 6.57 

Oxygen 0.03 


100.00 


HOT- AIR  ENGINES  AND    GAS-ENGINES.  21$ 

The  ideal  gas  which  would  be  produced  if  such  a  producer 
worked  perfectly  with  pure  carbon  is  given  for  the  sake  of 
comparison.  A  French  analysis  of  Dowson  gas  gave  over  II 
per  cent  of  carbon  dioxide. 

After  the  gas  is  formed  it  is  passed  through  a  scrubber  of 
coke  sprayed  with  water  to  cool  it  and  remove  the  large  pro- 
portion of  sulphur,  which  would  eventually  injure  the  cylinder. 
From  the  scrubber  the  gas  passes  to  a  gas-holder,  and  from 
the  holder  through  another  scrubber  to  the  engine.  This 
gas-producer  cannot  be  run  with  coal  which  produces  a  tarry 
distillate,  and  has  consequently  been  restricted  to  anthracite 
and  coke.  Other  producers  have  been  devised  which  are 
intended,  by  mingling  the  distillate  from  the  coal  with  steam 
and  passing  it  to  incandescent  fuel,  to  break  it  up  into  lighter 
compounds  like  marsh-gas  and  olefiant  gas.  Such  producers 
if  successful  could  use  bituminous  and  other  cheaper  coals. 

The  Dowson  gas,  from  its  composition,  requires  somewhat 
more  than  its  own  volume  of  air  for  complete  combustion,  and 
in  general  will  give  somewhat  less  mean  effective  pressure 
than  illuminating-gas.  Thus  a  scavenging-engine  with  Dow- 
son gas  gave  97.4  pounds  mean  effective  pressure,  while  with 
coal-gas  it  gave  113.5  pounds.  This  was  a  large  engine  with 
diameter  of  17  inches  and  a  stroke  of  24  inches;  smaller  en- 
gines may  be  expected  to  give  about  65  pounds  effective  pres- 
sure with  Dowson  gas. 

A  recent  test  by  Professor  Spangler  of  a  lOO-H.P.  Otto 
engine  using  gas  made  in  a  Taylor  producer  showed  that  the 
producer  developed  69  per  cent  of  the  heat  of  the  coal,  and 
that  the  engine  used  1.3  pounds  of  coal  per  horse-power  per 
hour  when  developing  130  horse-power.  The  coal  had  the 
following  composition : 

Moisture 4.20 

Volatile  matter 6.88 

Fixed  carbon 80.41 

Ash 8.5 1 

Sulphur , 0.74 

100.74       • 


2l6  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

A  test  by  Mr.  Dowson  of  a  Crossley  engine  showed  one 
pound  of  coal  per  horse-power  per  hour;  but  as  the  coal  in  the 
producer  was  estimated  at  the  beginning  and  end  of  the  test, 
and  as  the  test  was  only  eight  hours  long,  this  result  cannot 
be  accepted  without  question. 

Oil-engines. — A  volatile  oil  like  naphtha  or  gasoline, 
which  can  be  readily  vaporized  at  ordinary  temperatures,  can 
be  used  in  any  gas-engine.  It  is  sufficient  to  draw  a  part  of 
the  air-supply  through  some  simple  vaporizer  and  to  use  this 
mixture  of  air  and  vapor  in  place  of  gas.  But  there  is  danger 
that  such  volatile  oils  may  take  fire  accidentally  or  may  leak 
out  or  escape  from  tanks  and  reservoirs  and  mingle  with  air 
in  confined  spaces  and  form  an  explosive  mixture.  Though 
engines  of  some  size  have  been  run  with  gasoline,  the  applica- 
tion of  such  volatile  oils  to  explosive  engines  appears  to  be 
best  adapted  to  motor-carriages  or  to  small  open  boats  where 
there  is  less  danger  from  the  formation  of  explosive  mixtures 
with  air  in  confined  spaces.  Insurance  companies  in  America 
and  the  government  in  England  interfere  with  the  storing  and 
use  of  gasoline  and  other  volatile  oils,  and  so  have  checked 
their  use  in  gas-engines. 

Much  attention  has  been  given  in  England  to  the  develop- 
ment of  engines  which  can  use  refined  burning  oils  like  kero- 
sene. The  difficulty  in  the  use  of  such  oils  is  that  they  cannot 
be  entirely  vaporized  by  the  application  of  heat  alone  even 
though  raised  to  600°  F.  If  heated  under  pressure  they 
decompose,  and  yield,  together  with  a  light  volatile  product, 
another  product  which  is  heavier  than  the  original  oil.  If 
they  are  brought  to  a  very  high  temperature,  by  passing  over 
a  red-hot  surface  for  example,  they  are  likely  to  yield  car- 
bonaceous or  tarry  matter  which  clogs  the  vaporizer.  The 
only  exception  appears  to  be  the  oil  which  is  distilled  from 
Scotch  shales;  it  can  be  entirely  vaporized  at  about  570°  F., 
which  may  be  due  to  the  fact  that  it  is  made  by  a  destructive 
distillation. 

The  usual  way  of  treating  kerosene  and  other  safe  oils 


HOT-AIR  ENGINES  AND    GAS-ENGINES.  2I/ 

when  they  are  used  in  engines  is  to  spray  or  otherwise  mingle 
them  with  hot  air.  Three  ways  have  been  devised  for  doing 
this.  The  first  way  was  to  spray  the  oil  by  an  atomizer  into 
an  iron  cylinder,  which  was  heated  by  the  exhaust  gases  while 
the  engine  was  running.  The  air  for  the  engine  was  drawn 
through  this  cylinder,  and  thus  charged  with  oil  in  the  form  of 
vapor  or  perhaps  partly  in  a  spray  or  mist.  In  order  to  keep 
the  vaporizing  cylinder  hot  it  was  necessary  to  have  an  ex- 
plosion for  every  complete  cycle,  as  the  omission  of  an  explosion 
would  cool  the  vaporizer  too  much.  The  engine  was  governed 
by  reducing  simultaneously  the  oil  and  air-supply,  which  was 
found  to  be  a  very  wasteful  way. 

Another  way  of  accomplishing  the  same  thing  is  to  have 
an  extension  to  the  cylinder  which  is  not  cooled  by  a  water- 
jacket  and  which  consequently  becomes  strongly  heated.  This 
extension,  which  has  a  constricted  communication  with  the 
rest  of  the  cylinder,  is  filled  with  hot  spent  gases  after  an 
explosion,  into  which  the  oil  is  sprayed  and  by  which  it  is 
vaporized.  The  next  charge  of  air  is  compressed  into  the 
extension  to  the  cylinder,  mingles  with  the  hot  gases  in  it, 
and  an  explosive  mixture  is  formed  which  is  ignited  by  the 
heat  of  the  walls  or  the  heat  of  compression  when  the  proper 
proportions  are  attained.  A  variation  of  this  device  has  the 
entire  cylinder  cooled  with  a  water-jacket,  but  a  closed  recep- 
tacle smaller  than  the  cylinder  and  open  only  at  the  forward 
end  is  attached  to  the  cylinder-head.  This  receptacle  is  of 
course  heated  by  the  explosions,  and  can  vaporize  the  oil 
which  is  injected  into  the  hot  gases  remaining  in  it  after  the 
exhaust. 

The  third  and  perhaps  the  best  way  is  to  strongly  heat 
a  part  of  the  air  and  draw  it  through  oil  in  a  hot  vaporizer. 
This  method  brings  the  engine  into  much  the  condition  of  an 
engine  using  gasoline,  and  the  usual  way  of  governing  by 
omitting  explosions  can  be  used.  It  is  true  that  the  preced- 
ing method  may  be  governed  by  omitting  explosions,  but 
there  is  danger  that  the  hot  chamber  may  be  too  much  cooled 


218  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

if  several  explosions  are  omitted,  and  that  the  engine  will 
stop. 

All  methods  involving  the  use  of  hot  air  or  hot  gas  for 
vaporizing  the  oil  have  the  defect  that  the  charge  is  at  a  high 
temperature  before  it  is  compressed.  The  compression  must 
not  be  carried  too  far  for  fear  of  a  premature  explosion,  and 
again,  the  rise  of  temperature  is  less  than  for  a  cool  charge. 
Consequently  the  efficiency  of  the  engine  is  less  than  that  of 
a  gas-engine. 

The  id.eal  way  of  treating  safe  oils  for  use  in  an  explosive 
engine  appears  to  be  to  decompose  them  in  such  a  way  as  to 
get  volatile  products  only.  In  refining  petroleum  and  making 
kerosene  it  is  customary  to  treat  some  of  the  heavier  products 
by  distillation  and  redistillation  under  pressure,  and  thus  to 
gain  a  larger  proportion  of  illuminating-oil.  If  a  similar 
method  could  be  used  with  kerosene,  and  thus  a  volatile 
product  like  gasoline  could  be  made  continuously  as  demanded 
by  the  engine,  the  main  difficulty  with  the  use  of  safe  oils  in 
explosive  engines  would  be  removed. 

Ignition. — After  the  mixture  of  air  and  oil  is  compressed 
in  the  cylinder  of  an  explosion-engine  it  must  be  ignited. 
There  are  four  ways  of  accomplishing  this:  (i)  by  an  electric 
spark,  (2)  by  the  flame  method,  (3)  by  a  heated  tube,  and 
(4)  by  compression  in  a  hot  chamber. 

The  electric  method  requires  a  galvanic  battery,  an  in- 
duction-coil, and  a  circuit-breaker — apparatus  requiring  some 
care  and  intelligence.  It  appears  to  be  the  favorite  method 
in  America,  but  is  not  liked  in  England.  Older  forms  of  this 
device  had  simply  two  points  at  the  proper  distance  across 
which  a  spark  leaped  when  the  circuit  was  closed  or  broken  by 
a  circuit-breaker  outside  of  the  cylinder.  The  later  form  has 
the  circuit-breaker  inside  the  cylinder  consisting  of  two  points 
of  platinum,  one  of  which  is  pressed  against  or  wiped  over  the 
other  at  the  proper  time  by  a  gear  driven  by  the  engine.  A 
spark  is  formed  both  when  the  circuit  is  closed  and  when  it  is 
broken;  the  charge  is  usually  fired  by  the  spark  which  is 


HOT-AIR  ENGINES  AND    GAS-ENGINES.  219 

formed  when  the  circuit  is  opened  as  it  is  the  more  intense. 
This  apparatus  is  made  in  a  substantial  way  and  does  not 
appear  to  fail  or  give  trouble  in  any  way. 

The  flame  ignition  consists  in  conveying  an  ignited  mass 
of  gas  and  air  from  an  igniting  flame  outside  the  cylinder  of 
the  engine  to  the  explosive  mixture  inside.  The  space  or 
cavity  in  which  the  burning  gas  is  conveyed  is  usually  in  a 
slide  which  may  or  may  not  serve  as  the  valve  for  charging 
and  exhausting  the  cylinder.  To  convey  the  burning  gas  to 
the  charge  the  cavity  must  be  partially  filled  with  gas;  the 
gas  is  ignited  at  a  small  jet  burning  steadily  near  the  cylinder; 
the  cavity  is  then  closed  and  a  small  supply  of  explosive  gas 
from  the  cylinder  is  let  in  to  raise  the  pressure  in  the  cavity 
lest  the  sudden  opening  of  the  cavity  to  the  cylinder  should 
extinguish  the  flame;  the  cavity,  where  the  pressure  is  still 
less  than  in  the  cylinder,  is  brought  to  the  explosion-port  and 
the  charge  is  fired;  the  cavity  must  finally  be  ventilated  to  be 
ready  for  the  next  supply  of  gas.  This  method,  using 
illuminating  gas,  works  well  up  to  80  ignitions  a  minute. 
Clerk  has  a  flame  ignition  in  which  the  flame  cavity  is  fed  only 
from  the  compressed  explosive  gas  in  the  cylinder.  The 
cavity  consequently  does  not  require  ventilation  and  is  more 
quickly  filled  with  gas.  He  has  used  it  to  make  300  ignitions 
a  minute. 

The  hot  tube  requires  only  a  small  iron  tube,  which  is  kept 
red-hot  by  a  Bunsen  burner  or  other  heating  flame.  The 
tube  comes  out  horizontally  from  the  cylinder  and  sometimes 
is  turned  upward  for  convenience  in  heating.  At  the  proper 
time  the  explosive  mixture  in  the  cylinder  is  admitted  to  the 
tube  by  a  valve  which  is  worked  by  the  engine.  Sometimes 
the  tube  has  an  inlet-valve  at  the  outer  end  to  ventilate  the 
tube  with  air  drawn  in  during  the  filling  stroke. 

In  the  discussion  of  oil-engines  reference  has  already  been 
made  to  the  fact  that  the  charge  may  be  exploded  sponta- 
neously by  compressing  it  into  a  hot  receptacle.  In  some 
engines  this  occurs  when  the  hot  gas  with  its  charge  of  oil  in 


220  THERMODYNAMICS   OF   THE   STEAM-ENGINE, 

the  receptacle  is  mingled  with  a  proper  amount  of  air  to  form 
an  explosive  mixture.  In  other  engines  the  explosion  takes 
place  when  the  mixture  of  air  and  oil  is  compressed  to  a 
pressure  which  will  cause  an  explosion  in  contact  with  the  hot 
sides  of  the  receptacle  or  with  some  other  hot  metallic  surface. 
Considerable  ingenuity  has  been  shown  in  properly  propor- 
tioning oil-engines  so  that  the  explosion  shall  take  place 
spontaneously  at  the  proper  time.  This  method  is  better 
adapted  to  oil-engines  than  to  gas-engines,  as  a  mixture  of  oil 
and  air  is  more  readily  exploded  and  at  a  lower  temperature 
than  a  mixture  of  gas  and  air. 

Gas-engine  Governors. — The  only  effective  way  of  gov- 
erning a  gas-engine  is  to  omit  an  explosion  from  time  to  time, 
so  that  the  engine  shall  run  at  less  than  full  power.  When 
the  engine  is  running  light  two  or  more  explosions  in  succes- 
sion may  be  omitted.  When  the  engine  attains  too  high  a 
speed  the  governor  draws  back  the  cam  which  opens  the  gas- 
valve  and  no  gas  is  admitted;  the  engine  consequently  takes 
in  air  only,  compresses  and  expands  and  then  exhausts  it,  but 
no  work  is  developed  by  the  engine.  The  advantage  of  this 
method  is  that  the  engine  is  as  efficient  at  small  as  at  large 
loads;  owing  to  the  clearing  of  the  cylinder  of  spent  gases 
during  the  cycle  when  no  explosion  takes  place  the  succeed- 
ing working  cycle  is  more  efficient.  The  disadvantage  is  that 
the  engine  runs  irregularly,  as  the  only  source  of  energy  when 
the  engine  fails  to  explode  is  the  fly-wheel.  This,  and  the 
fact  that  only  one  stroke  in  four  is  a  working  stroke,  explains 
the  use  of  heavy  fly-wheels  for  explosive  engines. 

The  reason  why  the  engine  must  be  governed  by  omitting 
an  explosion  is  that  the  proportion  of  the  mixture  of  gas  and 
air  can  be  varied  only  within  narrow  limits  if  it  is  to  explode 
when  ignited.  Some  engines  for  electric  lighting  have  been 
made  to  diminish  the  gas-supply  when  the  load  is  smaller  than 
full  power,  but  the  variation  of  power  by  this  means  is  very 
small  and  must  be  supplemented  by  omitting  explosions  if  the 
load  is  much  diminished.  Large  gas-engines  with  two  cylinders 


HOT-AIR   ENGINES  AND    GAS-ENGINES. 


221 


are  of  course  more  easily  controlled  than  single-cylinder 
engines,  since  they  have  an  explosion  for  every  revolution. 

The  Diesel  Motor. — A  new  form  of  internal-combustion 
engine  was  described  by  Rudolf  Diesel  in  1893,  which  does 
away  with  many  of  the  difficulties  of  gas-  and  oil-engines  and 
which  at  the  same  time  gives  a  much  higher  efficiency.  The 
essential  feature  of  his  engine  consists  in  the  adiabatic  com- 
pression of  atmospheric  air  to  a  sufficient  temperature  to 
ignite  the  fuel  which  is  injected  at  a  determined  rate  during 
part  of  the  expansion  or  working  stroke.  The  first  experi- 
mental engines  were  built  at  Augsburg  in  1894  and  1896,  one 
of  12  and  another  of  20  horse-power;  now  the  construction 
of  these  engines  is  undertaken  at  several  places  in  Europe  and 
in  America. 

The  cycle  of  all  of  the  engines  thus  far  built  under 
Diesel's  patents  is  represented  by  Fig.  50,  which  represents 
four  strokes  of  a  single-acting  piston 
or  plunger.  Atmospheric  air  is 
drawn  in  from  a  to  b  and  is  com- 
pressed from  b  to  c  to  a  pressure  of 
500  pounds  to  the  square  inch  and  a 
temperature  of  1000°  F.  From  c  to 
d  fuel  is  injected  in  a  finely  divided 
form,  and  as  there  is  air  in  excess 
it  burns  completely  at  a  rate  that 
can  be  controlled  by  the  injection 
mechanism.  Thus  far  the  only  fuel 
used  is  petroleum  or  some  other  oil. 
At  d  the  supply  of  fuel  is  interrupted  FIG  50. 

and  the  remainder  of  the  working  stroke,  de,  is  an  adiabatic 
expansion.  The  cycle  is  completed  by  a  release  at  e  and  a 
rejection  of  the  products  of  combustion  from  b  to  a. 

The  cycle  has  a  resemblance  to  that  of  the  Otto  engine, 
but  differs  in  that  the  air  only  is  compressed  in  the  cylinder 
and  the  combustion  is  accompanied  by  an  expansion.  Diesel, 
in  his  theoretic  discussion  of  his  engine,  stipulates  that  the 


222  THERMODYNAMICS    OF   THE  STEAM-ENGINE. 

rate  of  combustion  shall  be  so  regulated  that  the  temperature 
shall  not  rise  during  the  injection  of  fuel,  and  that  the  line  cd 
shall  therefore  be  very  nearly  an  isothermal  for  a  perfect  gas. 
Since  the  fuel  is  added  during  the  operation  represented  by 
the  line  cd,  the  weight  of  the  material  in  the  cylinder  increases 
and  its  physical  properties  change,  so  that  the  line  will  not 
be  a  true  isothermal.  The  fact  that  there  is  air  in  excess 
makes  it  probable  that  these  changes  of  weight  and  properties 
will  be  insignificant.  On  the  other  hand,  it  is  not  probable 
that  in  practice  the  rate  of  injection  of  fuel  will  be  regulated 
so  as  to  give  no  rise  of  temperature,  or  that  there  is  'any  great 
advantage  in  such  a  regulation  if  the  temperature  is  not 
allowed  to  rise  too  high. 


FIG.  51. 

The  diagram  from  an  engine  of  this  type  is  shown  by 
Fig.  51,  which  appears  to  show  an  introduction  of  fuel  for 
one-eighth  or  one-seventh  of  the  working  stroke.  It  is  prob- 
able that  the  compression  and  the  expansion  after  the  cessa- 
tion of  the  fuel  supply  are  not  really  adiabatic,  though  as 
there  is  nothing  but  dry  gas  in  the  cylinder  during  those 
operations  the  deviation  may  not  be  large.  The  sides  and 
heads  of  the  cylinders  of  all  the  engines  thus  far  constructed 
are  water-jacketed,  though  the  use  of  such  a  water-jacket  and 
the  consequent  waste  of  heat  was  one  of  the  difficulties  in  the 
use  of  internal-combustion  engines  that  Diesel  sought  to 
avoid  by  controlling  the  rate  of  combustion. 


HOT-AIR  ENGINES  AND    GAS-ENGINES.  22$ 

The  oil  used  as  fuel  is  injected  in  form  of  a  spray  by  air 
that  is  compressed  separately  in  a  small  pump  to  30  or  40 
pounds  pressure  above  that  in  the  main  cylinder;  of  course  it 
is  necessary  to  cool  this  portion  of  the  air  after  compression 
to  avoid  premature  ignition.  The  engines  that  have  been 
used  are  described  as  giving  a  clear  and  nearly  dry  exhaust. 
In  damp  weather  the  exhaust  shows  a  little  moisture,  prob- 
ably from  the  combustion  of  hydrogen  in  the  oil.  The 
cylinder  when  opened  shows  a  slight  deposit  of  soot  on  the 
head.  It  appears  therefore  that  Diesel  has  succeeded  in 
constructing  an  engine  for  burning  heavy  oils  with  good 
economy  and  without  the  annoyances  of  an  igniting  device. 
The  engines  have  the  further  advantage  in  that  the  work  can 
be  regulated  by  the  amount  of  fuel  supplied,  which  amount  is 
not  controlled,  as  in  explosive  engines,  by  the  necessity  to 
form  an  explosive  mixture.  The  discussion  of  the  theoretical 
efficiency  of  the  cycle  shows  that  the  efficiency  ^increases  as 
the  time  of  injection  of  fuel  is  shortened.  In  practice  the 
engine  shows  a  slight  decrease  in  economy  for  light^oads,  due 
probably  to  the  losses  by  radiation  and  to  the  wafer- jacket, 
which  are  nearly  constant  for  all  loads. 

In  the  exposition  of  the  theory  of  his  motor,  Diesel  * 
claims  that  all  kinds  of  fuel,  solid,  liquid,  and  gaseous,  can  be 
burned  in  his  motor.  As  yet  oil  only  has  been  used;  the 
choice  of  petroleum  or  other  heavy  oil  has  probably  been  due 
to  the  low  cost  of  such  oils.  It  is  evident  that  gas  may  be 
used  in  this  type  of  engine;  the  gas  can  be  compressed 
separately  to  a  pressure  somewhat  higher  than  that  in  the 
main  cylinder,  much  as.  the  air  is  which  is  used  for  injecting 
oil.  It  does  not  appear  necessary  to  cool  the  gas  after  com- 
pression, as  it  will  burn  only  when  supplied  with  air. 

There  appears  to  be  no  insurmountable  difficulty  in  sup- 
plying powdered  solid  fuel  to  this  engine.  The  presence  of 
the  ash  from  such  fuel  in  the  cylinder  may,  however,  be 
expected  to  give  trouble.  Diesel  claims  that  with  a  large 
*  Rational  Heat  Motor\  Rudolf  Diesel,  trans.  Bryan  Donkin. 


224  THERMODYNAMICS   OF   THE   STEAM-ENGINE, 

excess  of  air  (for  example,  a  hundred  pounds  of  air  for  one 
pound  of  coal)  the  ash  will  be  swept  out  of  the  cylinder  with 
the  spent  gases  and  will  not  give  trouble;  but  that  claim  is 
accompanied  by  an  assumption  that  air  may  be  compressed 
isothermally  if  water  is  injected  into  the  cylinder  of  the  com- 
pressor, and  one  idea  appears  to  be  as  improbable  as  the 
other. 

All  the  engines  thus  far  built  have  single-acting  pistons  or 
plungers  which  perform  all  four  operations  for  a  cycle  in  one 
cylinder.  Some  of  the  engines  have  three  cylinders  with 
their  plungers  connected  to  a  three-throw  crank-shaft ;  but  in 
that  case  each  plunger  has  its  own  complete  cycle  performed 
in  four  strokes,  just  as  for  the  single-cylinder  engine.  Diesel 
has,  however,  described  a  compound  engine  which  has  both 
compression  and  expansion  divided  into  two  stages.  Such 
an  engine  may  have  a  compression-pump,  a  combustion- 
cylinder,  and  an  expansion-cylinder.  The  pump  takes  air 
from  the  atmosphere  and  compresses  it  to  a  moderate  pressure 
and  delivers  it  to  a  receiver.  The  combustion-cylinder  has  a 
plunger  like  that  of  the  simple  engine  which  performs  a  cycle 
in  four  strokes.  It  takes  air  at  nearly  constant  pressure  from 
the  receiver  on  the  first  down  stroke  and  compresses  it  to  the 
proper  pressure  and  temperature  to  ignite  the  fuel  on  the  fol- 
lowing up  stroke;  during  a  part  of  the  second  down  stroke 
fuel  is  injected  at  such  a  rate  as  to  produce  isothermal  expan- 
sion, and  the  remainder  of  that  stroke  gives  adiabatic  ex- 
pansion with  a  reduction  of  temperature;  the  products  of 
combustion  cooled  to  a  considerable  extent  by  the  partial 
adiabatic  expansion  in  the  combustion-cylinder  are  transferred 
to  the  expansion-cylinder  during  the  fourth  stroke  of  the 
plunger,  which  completes  the  cycle  of  the  combustion-cylinder. 
The  proportions  of  the  three  cylinders  should  be  such  that 
the  fourth  stroke  of  the  plunger  just  mentioned  should  have 
for  its  terminal  pressure  the  pressure  in  the  receiver.  The 
expansion-cylinder  completes  the  expansion  of  the  products 
of  combustion  and  then  discharges  them  into  the  atmosphere; 


HOT-AIR   ENGINES  AND    GAS-ENGINES.  22$ 

by  its  use  the  final  volume  of  those  gases  when  release  occurs 
may  be  greater  than  the  volume  of  the  air  drawn  in  by  the 
compression-pump,  and  if  desired,  the  expansion  may  be  car- 
ried down  to  the  pressure  of  the  atmosphere.  By  assuming 
an  isothermal  compression  in  the  compression-pump,  Diesel 
works  out  a  theoretic  cycle  which  approaches  very  closely  in 
appearance  and  efficiency  to  Carnot's  cycle  for  a  perfect  gas; 
it  appears  that  his  attention  was  first  directed  to  the  motor  he 
has  invented  by  an  attempt  to  describe  an  engine  which  could 
work  on  Carnot's  cycle.  But  he  assumes  that  an  isothermal 
compression  can  be  obtained  by  simply  spraying  water  into 
the  pump-cylinder  during  compression,  which  is  contrary  to 
experience  in  the  use  of  air-compressors.  Even  if  such  an 
isothermal  compression  were  practicable,  it  is  doubtful  whether 
it  would  be  desirable;  as  it  would  require  a  much  higher 
pressure  to  produce  the  proper  ignition  temperature  in  the 
combustion-cylinder  than  is  now  employed  in  single-cylinder 
engines;  but  the  high  pressure  required  to  give  ignition  is  one 
of  the  principal  sources  of  difficulty  in  the  single  engine. 

Since  both  compression-pump  and  expansion-cylinder, 
even  with  single-acting  pistons,  will  have  one  working  stroke 
for  each  revolution,  while  the  combustion-cylinder  can  give  a 
working  stroke  for  two  revolutions,  it  is  clear  that  the  com- 
pound engine  must  have  at  least  two  combustion-cylinders 
with  their  plungers  working  together,  but  having  their  opera- 
tions half  a  cycle  apart.  The  expansion-piston  should  have 
its  crank  opposite  those  of  the  combustion-plungers.  The 
compression-pump  may  have  its  crank  set  at  any  convenient 
angle,  since  it  delivers  air  to  a  reservoir. 

A  theoretical  discussion  of  the  efficiency  of  the  cycle  for 
the  simple  engine  as  represented  by  Fig.  50  may  be  obtained 
by  considering  that  heat  is  added  at  constant  temperature 
from  c  to  d  and  that  heat  is  rejected  at  constant  volume  from 
e  to  b,  bearing  in  mind  that  be  and  dc  represent  adiabatic 
changes. 

From  equation  (75),  page  65,  the  expression  for  the  heat 


226          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

supplied  from  c  to  d  is,  for  one  pound  of  working  substance, 
a  =  Apcvc  log,  -'  =  ARTC  log,  -*. 

^r  ^ 

The  heat  rejected  at  constant  volume  is 

Q,  =  c,(Tf-  Tt)  =  c->(Tt-  7i). 

/C 

Since  the  expansion  de  is  adiabatic, 


but  since  the  compression  be  is  also  adiabatic, 


and  consequently 


for  v,  =  ^.      Replacing  Te  by  its  value  in  the  expression  for 
<2a,  we  have 


Finally,  the  efficiency  appears  to  be 

II;  ,  «.-<>.  . 

01  ^/c^r,ioge-rf 

Inspection  of  the  equation  shows  that  the  efficiency  may 
be  increased  by  raising  the  temperature  Tc  or  by  reducing  the 
temperature  T6.  The  latter  is  practically  the  temperature  of 
the  atmosphere,  but  Te  may  be  made  any  desired  temperature 
by  reducing  the  clearance  of  the  cylinder  and  thus  raising  the 
pressure  at  the  end  of  compression.  Again,  the  efficiency 


HOT-AIR   ENGINES  AND    GAS-ENGINES.  22/ 

may  be  increased  by  reducing  the  time  during  which  fuel  is 
injected,  that  is,  by  reducing  the  ratio  vd  :  vc,  as  may  be 
proved  by  a  series  of  calculations  with  different  values  for  that 
ratio.  This  is  a  very  important  conclusion,  as  it  shows  that 
the  engine  will  have  in  practice  little  if  any  falling  off  in 
efficiency  at  reduced  loads. 

It  is  reported  that  a  clearance  of  something  less  than  7  per 
cent  is  associated  with  a  compression  to  500  pounds  and  a 
temperature  of  1000°  F.,  or  more.  Taking  the  pressure  of 
the  atmosphere  at  14.7  pounds  per  square  inch,  adiabatic 
compression  to  500  pounds  above  the  atmosphere  or  to  514.7 
pounds  absolute  requires  a  clearance  of 


= 0.0796,, 


so  that  the  clearance  is 

0.0796  -i-  {  i  —  0.0796  j  =  0.0865 

the  piston  displacement. 

If  the  temperature  of  the  atmosphere  be  taken  at  70°  F. 
or  53°-7  absolute,  the  temperature  after  adiabatic  compres 
sion  becomes 


absolute,  or  1020°  F. 

If  it  be  further  assumed  that  fuel  is  supplied  for  one-tenth 
of  the  working  stroke,  then 

• 

vd  —  o.\(vb  —  v^)  -f  va  =  0.1(1  —  0.0796)  +  0.0796^ 

=  0.1716^. 

; 

The  equation  for  efficiency  gives  in  this  case 


228  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

(  /O.I7l6\°-«°5  ) 

778X0.2375X530.7^)         -' 

rf—l o  i   16      =0-58- 

1.405  X  53.22  X  1480  log,0'171,. 

0.0796 

An  engine  giving  26.6  indicated   horse-power  (cheval-a 
vapeur)  and  exerting  19.2  horse-power  at  the  brake  is  reportec 
to  consume  223  grams  of  petroleum  per  hour  and  to  give  a 
thermal  efficiency  of  28.6   per  cent.      Now  if  the   heats   o 
combustion  of  coal  and  petroleum  are  taken  at  i4©€r~B.  T.  u 
and  20,000  B.  T.  U.,  respectively,  one  gram  of  petroleum  is 
equivalent  to  -V0-  of  a  gram  of  coal,  and  the  performance  o 
the  Diesel  engine  is  equal  to  the  consumption  of  333  grams 
of  coal  per  horse-power  per  hour,  or  to  about  f  of  a  pound  o 
coal  per  English  horse-power  per  hour.     To  make  the  com 
parison   complete   the  relative  costs  of  coal  and   petroleum 
should  be  considered,   together  with  the   probability  that  a 
large  demand  for  petroleum  would  be  liable  to  affect  its  price 


CHAPTER    XI. 
THE   STEAM-ENGINE. 

THE  steam-engine  is,  at  the  present  time,  the  most  im- 
portant heat-engine.  When  of  large  size  and  properly 
designed  and  managed  it  has  at  least  as  good  economy  as 
any  other  heat-engine,  though  it  may  be  excelled  in  this 
regard  by  explosive  gas-engines  when  they  are  fully  devel- 
oped. It  can  be  controlled,  regulated,  and  reversed  easily 
and  positively — properties  which  are  not  possessed  in  like 
degree  by  other  heat-engines.  It  is  interesting  to  know  that 
the  theory  of  thermodynamics  was  developed  mainly  to 
account  for  the  action  and  to  provide  methods  of  designing 
steam-engines;  though  neither  object  is  entirely  accom- 
plished, on  account  of  the  fact  that  the  engine-cylinder  must 
be  made  of  some  metal  to  be  hard  and  strong  enough  to 
endure  service,  for  all  metals  are  good  conductors  of  heat  and 
seriously  affect  the  action  of  a  condensable  fluid  like  steam. 

Carnot's  Cycle  for  a  steam-engine  is  represented  by  Fig. 
52,  in  which  ab  and  cd  are  isothermal  lines    j 
representing  the  application  and  rejection 
of    heat  at  constant    temperature    and    at 
constant  pressure,     be  and  da  are  adiabatic 
lines,  representing  change  of  temperature 
and  pressure,  without  transmission  of  heat 
through   the  walls   of   the  cylinder.      The 
diagram    representing    Carnot's   cycle  has 
an  external  resemblance  to  the  indicator- 
diagram  from  some  actual  engines,  but  it  differs  in  essential 
particulars. 

229 


230  THERMODYNAMICS    OF   THE   STEAM-ENGINE. 

In  the  condition  represented  by  the  point  a  the  cylinder 
contains  a  mixture  of  water  and  steam  at  the  temperature  ^ 
and  the  pressure/^  If  connection  is  made  with  a  source  of 
heat  at  the  temperature  t^  and  heat  is  added,  some  of  the 
water  will  be  vaporized  and  the  volume  will  increase  at  con- 
stant pressure  as  represented  by  ab.  If  thermal  communica- 
tion is  now  interrupted  adiabatic  expansion  may  take  place  as 
represented  by  be  till  the  temperature  is  reduced  to  t^  the 
temperature  of  the  refrigerator,  with  which  thermal  com- 
munication may  now  be  established.  If  the  piston  is  forced 
toward  the  closed  end  of  the  cylinder  some  of  the  steam  in  it 
will  be  condensed,  and  the  volume  will  be  reduced  at  constant 
pressure  as  represented  by  cd.  The  cycle  is  completed  by  an 
adiabatic  compression  represented  by  da, 

If  the  absolute  temperature  of  the  source  of  heat  is  T19 
and  if  that  of  the  refrigerator  is  7!,,  then  the  efficiency  is 

y.  -  T, 

n=   -r-, 


whatever  may  be  the  working  fluid. 

For  example,  if  the  pressure  of  the  steam  during  isother- 
mal expansion  is  100  pounds  above  the  atmosphere,  and  if  the 
pressure  during  isothermal  compression  is  equal  to  that  of  the 
atmosphere,  then  the  temperatures  of  the  source  of  heat  and 
of  the  refrigerator  are  337°.  6  F.  and  212°  F.,  or  798.4  and 
672.7  absolute,  so  that  the  efficiency  is 


The  following  table  gives  the  efficiencies  worked  out  in  a 
similar  way,  for  various  steam-pressures,  —  both  for  /a  equal  to 
212°  F.,  corresponding  to  atmospheric  pressure,  and  for  /, 
equal  to  116°  F.,  corresponding  to  an  absolute  pressure  of 
1.5  pounds  to  the  square  inch: 


THE  STEAM-ENGINE.  2 

EFFICIENCY   OF   CARNOT'S   CYCLE    FOR   STEAM-ENGINES. 


Initial  Pressure 

by  the  Gauge, 
above  the 

Atmospheric 
Pressure. 

1.5  Pounds 
Absolute. 

Atmosphere. 

15 

0-053 

O.l8q 

30 

0.084 

0.215 

60 

0.124 

0.249 

100 

0-157 

0.278 

150 

0.186 

0.302 

2OO 

0.207 

0.320 

300 

0.238 

0-347 

The  column  for  atmospheric  pressure  may  be  used  as  a 
standard  of  comparison  for  non-condensing  engines,  and  the 
column  for  1.5  pounds  absolute  may  be  used  for  condensing 
engines. 

It  is  interesting  to  consider  the  condition  of  the  fluid  in 
the  cylinder  at  the  different  points  of  the  diagram  for  Carnot's 
cycle.  Thus  if  the  fluid  at  the  condition  represented  by  b 
in  Fig.  52  is  made  up  of  xb  part  steam  and  I  —  xb  part  water, 
then  from  equation  (146)  the  condition  at  the  point  c  is  given 
by 


In  like  manner  the  condition  of  the  mixture  at  the  point  d  is 


(245) 


It  is  interesting  to  note  that  if  xb  is  larger  than  one-half, 
that  is,  if  there  is  more  steam  than  water  in  the  cylinder  at  b, 
then  the  adiabatic  expansion  is  accompanied  by  condensation. 
Again,  if  xa  is  less  than  one-half,  then  the  adiabatic  compres- 
sion is  also  accompanied  by  condensation.  Very  commonly 
it  is  assumed  that  xb  is  unity,  so  that  there  is  dry  saturated 
steam  in  the  cylinder  at  b  ;  and  that  xa  is  zero  so  that  there 
is  water  only  in  the  cylinder  at  a\  but  there  is  no  necessity 
for  such  assumptions,  and  they  in  no  way  affect  the  efficiency. 


232  THERMODYNAMICS   OF   THE   STEAM-ENGINE, 

If  the  cylinder  contains  M  pounds  of  steam  and  water,  the 
heat  absorbed  by  the  working  substance  during  isothermal 
expansion  is 

&  =  Mr,(xb  -  O,  .      ...    ...     (246) 

and  the  heat  rejected  during  isothermal  compression  is 

(2,  =  Mr,(xc  -  xd), (247) 

so  that  the  heat  changed  into  work  during  the  cycle  is 

Ci  -  C.  =  M\ r,(x.  -  xt)  -  r&e  -*,){.     .     (248) 
But  from  equations  (244)  and  (245) 

7* 
r^(xe  —  *d)  =  fri(x*  —  *«)>       •      •      •      (249) 

and  the  expression  for  the  heat  changed  into  work  becomes 
<2,  -  fi.  =  Urfct  -  x«)  ^~^-'.       .     .     (2  so) 

•*•   \ 

This  equation  is  deduced  because  it  is  convenient  for  making 
comparisons  of  various  other  volatile  liquids  and  their  vapors, 
with  steam,  for  use  in  heat-engines.  It  is  of  course  apparent 
that 

_  &  ~  6.  _  T>  -  T, 
<2,  T,      ' 

from  equations  (250)  and  (246),  a  conclusion  which  is  known 
independently,  and  indeed  is  necessary  in  the  development 
of  the  theory  of  the  adiabatic  expansion  of  steam, 

In  the  discussion  thus  far  it  has  been  assumed  that  the 
working  fluid  is  steam,  or  a  mixture  of  steam  and  water.  But 
a  mixture  of  any  volatile  liquid  and  its  vapor  will  give 
similar  results,  and  the  equations  deduced  can  be  applied 


THE   STEAM-ENGINE.  233 

directly.  The  principal  difference*  will  be  due  to  the 
properties  of  the  vapor  considered,  especially  its  specific 
pressures  and  specific  volumes  for  the  temperatures  of  the 
source  of  heat  and  the  refrigerator. 

For  example,  the  efficiency  of  Carnot's  cycle  for  a  fluid 
working  between  the  temperatures  160°  C.  and  40°  C.  is 

160  —  40 

=  0.277. 


1 60  +  273.7 

The  properties  of  steam  and  of  chloroform  at  these  tem- 
peratures are 

Steam.  Chloroform. 

40°  C.  i6o°C.  40°  C.  i6o«C. 

Pressure,  mm.  mercury 54-91       4651.4  369.26         8734.2 

Volume,  cubic  metres 19-74             0.3035             0.4449           0.0243 

Heat  of  vaporization,  r 578.7           494-2  63.13             50.53 

Entropy  of  liquid,  0 0.1364         0.4633             0.03196         0.11041 

For  simplicity,  we  may  assume  that  one  kilogram  of  the 
fluid  is  used  in  the  cylinder  for  Carnot's  cycle,  and  that  xb  is 
unity  while  xa  is  zero,  so  that  from  equation  (250) 

T  -     T 
Ql-Q,  =  rl±~L', 

2  1 

and  for  steam 

G,  —  G,  =  494-2  X  0.277  =  137  calories, 
while  for  chloroform 

G,  —  <2,  =  50.53  X  0.277  =  H  calories. 

After  adiabatic  expansion  the  qualities  of  the  fluid  will  be, 
from  equation  (244),  for  steam 

40+ 


578, 


234  THERMODYNAMICS    OF   THE   STEAM-ENGINE. 

and  for  chloroform 

40  +  273.7;   50.53  \ 

.r  — --J— -^-^  ^  , h  0.11041  —  0.03196]  =0.960. 

63.13     Vi6o+273.7n  *  y 

The  specific  volumes  after  adiabatic  expansion  are,  conse- 
quently, for  steam 

ve  =  xcu,  +  ff  =  0.795(19.74  -  o.ooi)  +  o.ooi  =  15.7, 
and  for  chloroform 

vc  =  xcu^-\-  o-  =  0.969(0.4449  —  0.000655)  +  0.000655  =  0.431. 

These  values  for  vc  just  calculated  are  the  volumes  in  the 
cylinder  at  the  extreme  displacement  of  the  piston,  on  the 
assumption  that  one  kilogram  of  the  working  fluid  is  vaporized 
during  isothermal  expansion.  A  better  idea  of  the  relative 
advantages  of  the  two  fluids  will  be  obtained  by  finding  the 
'heat  changed  into  work  for  each  cubic  metre  of  maximum 
piston-displacement,  or  for  a  cylinder  having  the  volume  of 
one  cubic  metre.  This  is  obtained  by  dividing  <2,  —  Qa,  the 
heat  changed  into  work  for  each  kilogram  by  vc.  For  steam 
the  result  is 

(a  -  a)  -*-  Vc  =  137  ^  157  =  8.73, 
and  for  chloroform  it  is 

(a  -  a)  •*•  *>c  =  14  -f-  0.413  =  34 ; 

from  which  it  appears  that  for  the  same  volume  chloroform 
can  produce  more  than  three  and  a  half  times  as  much  power. 
Even  if  we  consider  that  the  difference  of  pressure  for  chloro- 
form, 

8734.2  —  369.3  =  8364.9  mm., 
is  nearly  twice  that  for  steam,  which  has  only 
4651.4  -  54.9  =  4596.5  mm. 


THE   STEAM-ENGINE. 

difference  of  pressure,  the  advantage  appears  to  be  in  favor 
of  chloroform.  If,  however,  the  difference  of  pressures  given 
for  chloroform  is  allowable  also  for  steam,  giving 

8364.9  +  54.9  =  8419.8  mm. 

for  the  superior  pressure,  then  the  initial  temperature  for 
steam  becomes  184°.  9  C.,  and  the  efficiency  becomes 


184.9+273-7 

instead  of  0.277.  On  the  whole,  steam  is  the  more  desirable 
fluid,  even  if  we  do  not  consider  the  inflammable  and  poison- 
ous nature  of  chloroform.  Similar  calculations  will  show  that 
on  the  whole  steam  is  at  least  as  well  adapted  for  use  in  heat- 
engines  as  any  other  saturated  fluid  ;  in  practice,  the  cheap- 
ness and  incombustibility  of  steam  indicate  that  it  is  the 
preferable  fluid  for  such  uses. 

Non-conducting  Engine.  —  The  conditions  required  for 
alternate  isothermal  expansion  and  adiabatic  expansion  cannot 
be  fulfilled  for  Carnot's  cycle  with  steam  any  more  than  they 
could  be  for  air.  The  diagram  for  the  cycle  with  steam, 
however,  is  well  adapted  to  production  of  power;  the  con- 
trary is  the  case  with  air,  which  gives  a  much  attenuated 
diagram. 

In  practice  steam  from  a  boiler  is  admitted  to  the  cylinder 
of  the  steam-engine  during  that  part  of  the  cycle  which 
corresponds  to  the  isothermal  expansion  of  Carnot's  cycle, 
thus  transferring  the  isothermal  expansion  to  the  boiler,  where 
steam  is  formed  under  constant  pressure.  In  like  manner 
the  isothermal  compression  is  replaced  by  an  exhaust  at  con- 
stant pressure,  during  which  steam  may  be  condensed  in  a 
separate  condenser,  cooled  by  cold  water. 

By  proper  valve-gear  the  expansion  and  compression  of 
Carnot's  cycle  may  be  simulated,  thus  giving  a  diagram  hav- 
ing an  external  resemblance  to  Carnot's  cycle.  The  cylinder 


236  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

is  commonly  made  of  cast  iron,  and  is  always  some  kind  of 
metal;  there  is  consequently  considerable  interference  due  to 
the  conductivity  of  the  walls  of  the  cylinder,  and  the  expan- 
sion and  compression  are  never  adiabatic.  There  is  an  advan- 
tage, however,  in  discussing  first  an  engine  with  a  cylinder 
made  of  some  non-conducting  material,  although  no  such 
material  proper  for  making  cylinders  is  now  known. 

The  diagram   representing  the  operations   in   a   non-con- 
ducting cylinder  for  a  steam-engine  can  be  represented  by 
Fig.    53-      ab   represents   the   admission   of 
dry  saturated  steam   from  the  boiler;   be  is 
an     adiabatic    expansion    to     the     exhaust 
pressure;    cd  represents   the   exhaust;    and 
da  is  an  adiabatic  compression  to  the  initial 
FlG-  53'  pressure.       It    is    assumed    that    the   small 

volume,  represented  by  a,  between  the  piston  and  the  head 
of  the  cylinder  is  filled  with  dry  steam,  and  that  the  steam 
remains  homogeneous  during  exhaust  so  that  the  quality  is 
the  same  at  d  as  at  c.  These  conditions  are  consistent  and 
necessary,  since  the  change  of  condition  due  to  adiabatic 
expansion  (or  compression)  depends  only  on  the  initial  condi- 
tion and  the  initial  and  final  pressures;  so  that  an  adiabatic 
expansion  from  a  to  d  would  give  the  same  quality  at  d  as 
that  found  at  c  after  adiabatic  expansion  from  b*  and  con- 
versely adiabatic  compression  from  d  to  a  gives  dry  steam  at 
a  as  required. 

The  cycle  represented  by  Fig.  53  differs  most  notably 
from  Carnot's  cycle  (Fig.  52)  in  that  ab  represents  admission 
of  steam  and  cd  represents  exhaust  of  steam,  as  has  already 
been  pointed  out.  It  also  differs  in  that  the  compression  da 
gives  dry  steam  instead  of  wet  steam.  The  compression  line 
da  is  therefore  steeper  than  for  Carnot's  cycle,  and  the  area  of 
the  figure  is  slightly  larger  on  this  account.  This  curious  fact 
does  not  indicate  that  the  cycle  has  a  higher  efficiency;  on 
the  contrary,  the  efficiency  is  less,  and  the  cycle  is  incom- 
plete. To  complete  the  cycle  for  a  non-conducting  cylinder 


THE   STEAM-ENGINE.  237 

the  exhausted  steam   must  be  condensed,  pumped  back  into 
the  boiler,  and  reevaporated. 

If  the  pressure  during  admission  (equal  to  the  pressure  in 
the  boiler)  is/,,  and  if  the  pressure  during  exhaust  is/3,  then 
the  heat  required  to  raise  the  water  resulting  from  the  con- 
densation of  the  exhaust-steam  is 


where  q,  is  the  heat  of  the  liquid  at  the  pressure  /t  and  q^  is 
the  heat  of  the  liquid  at  the  pressure  /,.  The  heat  of  vapori- 
zation at  the  pressure/,  is  r^  so  that  the  heat  required  to  raise 
the  feed-water  from  the  temperature  of  the  exhaust  to  the 
temperature  in  the  boiler  and  evaporate  it  into  dry  steam  is 

G,  =  r,  +  &-?,;     •    ••  •    •    •    (250 

and  this  is  the  quantity  of  heat  supplied  to  the  cylinder  per 
pound  of  steam. 

The  steam  exhausted  from  the  cylinder  has  the  quality  x^ 
calculated  by  aid  of  the  equation 


and  the  heat  that  must  be  withdrawn  when  it  is  condensed  is 

<2,  =  *,'>,  ........    (252) 

this  is  the  heat  rejected  from  the  engine.     The  heat  changed 
into  work  per  pound  of  steam  is 

Gi  —  G,  =  ',  +  ?,-?.—  *fr      -     •     •     (253) 

But  part  of  the  work  is  used  in  pumping  the  condensed 
steam  or  feed-water  into  the  boiler  from  the  pressure  /,  to 
the  pressure/,.  The  heat  equivalent  of  this  work  is 

AH      ......     (254) 


where  o"  is  the  specific  volume  of  water.     This  heat  should 
be  subtracted  from  the  heat  changed  into  work  per  pound  of 


238  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

steam  to  find  the  available  energy  developed  by  the  engine. 
But   the  heat  represented  by  the   expression  (254)  is  small 
compared  with  the  heat  changed  into  work  as  represented  by 
equation  (253),  and  may  be  neglected. 
The  efficiency  of  the  cycle  is 


If  values  are  assigned  to/,  and/a  and  the  proper  numeri- 
cal calculations  are  made,  it  will  appear  that  the  efficiency  for 
a  non-conducting  engine  is  always  less  than  the  efficiency  for 
Carnot's  cycle  between  the  corresponding  temperatures. 

It  should  be  remarked  that  the  efficiency  is  not  affected 
by  the  clearance  or  space  between  the  piston  and  the  head  of 
the  cylinder  and  the  space  in  the  steam-passages  of  the 
cylinder,  provided  that  the  clearance  is  filled  with  dry  sat- 
urated steam  as  indicated  in  Fig.  52.  This  is  evident  from 
the  fact  that  no  term  representing  the  clearance,  or  volume 
at  #,  Fig.  52,  appears  in  equation  (254).  Or,  again,  we  may 
consider  that  the  steam  in  the  cylinder  at  the  beginning  of 
the  stroke,  occupying  the  volume  represented  by  a,  expands 
during  the  adiabatic  expansion  and  is  compressed  again  dur- 
ing compression,  so  that  one  operation  is  equivalent  to  and 
counterbalances  the  other,  and  so  does  not  affect  the  efficiency 
of  the  cycle. 

Incomplete   Cycle.  —  The    cycle    for    a    non-conducting 
engine    may   be    incomplete    because   the    expansion    is    not 
carried  far  enough  to  reduce  the  pres- 
sure to  that  of  the  back-pressure  line, 
as  is  shown   in   Fig.  54.      Such  an  in- 
complete cycle  has  less  efficiency  than 
_   a  complete  cycle,  but   in   practice   the 
advantage  of  using  a  smaller  cylinder 


and   of   reducing   friction    is    sufficient 

compensation  for  the  small  loss  of  efficiency  due  to  a  moderate 
drop  at  the  end  of  the  stroke,  as  shown  in  Fig.  54. 


THE   STEAM-ENGINE.  239 

The  discussion  of  the  incomplete  cycle  is  simplified  by 
assuming  that  there  is  no  clearance  and  no  compression  as  is 
indicated  by  Fig.  54.  It  will  be  shown  later  that  the 
efficiency  will  be  the  same  with  a  clearance,  provided  the 
compression  is  complete. 

The  most  ready  way  of  finding  the  efficiency  for  this  cycle 
is  to  determine  the  work  of  the  cycle.  Thus  the  work  dur- 
ing admission  is 


(256) 


where  ul  is  the  increase  of  volume  due  to  vaporization  of  a 
pound  of  steam  and  <r  is  the  specific  volume  of  water.  The 
work  during  expansion  is 


-  EC  =  ~(P,  +  ?i  -  xcpc  -  qc\  .     .     .     (257) 


where  gl  and  />,  are  the  heat  of  the  liquid  and  the  heat-equiv- 
alent of  the  external  work  during  vaporization  at  the  pressure 
/,,  while  qc  and  pc  are  corresponding  quantities  for  the 
pressure  at  c.  xc  is  to  be  calculated  by  the  equation 


The  work  done  by  the  piston  on  the  steam  during  ex 
haust  is 

v.    i 


The  total  work  of  the  cycle  is  obtained  by  adding  the 
work  during  admission  and  expansion  and  subtracting  the 
work  during  exhaust,  giving 


(A  -  AK     (258) 


240  THERMOD  YNAMICS   OF   THE   STEAM-ENGINE. 

The  last  term  is  small,  and  may  be  neglected.  Adding  and 
subtracting  Apcxcuc  and  multiplying  by  A,  we  get  for  the 
heat-equivalent  of  the  work  of  the  cycle 

<2.  -  (2,  =  r,  -  xcrc  +  A(pc  -  />«*,  +  q,  -  qc,    .     (259) 

which  is  equal  to  the  difference  between  the  heat  supplied 
and  the  heat  rejected  as  indicated.  The  heat  supplied  is 

G,  =  ^  +  &  -  ft, 

as  was  deduced  for  the  complete  cycle;  the  cost  of  making 
the  steam  remains  the  same,  whether  or  not  it  is  used  effi- 
ciently. Finally,  the  efficiency  of  the  cycle  is 

_  &  —  (2,  __  r»  +  q,  -xcrc  -  qc  +  A(pc  —  p^xcuc 

a  r>  +  ft  -  <?> 


...  _  ---  (26o) 

r>  +  ft  -  9* 

If  pc  is  made  equal  to/a  in  the  preceding  equation,  it  will 
be  reduced  to  the  same  form  -as  equation  (254),  because  the 
cycle  in  such  case  becomes  complete. 

Steam-consumption  of  Non-conducting  Engine.  —  A 
horse-power  is  33000  foot-pounds  per  minute  or  60  X  33000 
foot-pounds  per  hour.  But  the  heat  changed  into  work  per 
pound  of  steam  by  a  non-conducting  engine  with  complete 
expansion  is,  by  equation  (253), 

r^  +  9,  —  WV,» 
so  that  the  steam  required  per  horse-power  per  hour  is 

60  X  33°QQ  _ 
,  +  q,  -  q,  -  x,r,)' 


THE   STEAM-ENGINE.  241 

Similarly,  the  steam  per  horse-power  per  hour  for  an  engine 
with  incomplete  expansion,  by  aid  of  expression  (258),  is 

60  X  33QQQ 


f  Apji,  —  xcpc  —  Ap^xciic  +  ft  —  ft) 

The  value  of  x^  or  xe  is  to  be  calculated  by  the  general  equa- 
tion 

Tfr 
x  —  - 


The  denominator  in  either  of  the  above  expressions  for  the 
steam  per  horse-power  per  hour  is  of  course  the  work  done 
per  pound  of  steam  and  the  parenthesis  without  the  mechan- 
ical equivalent  778  is  equal  to  <2,  —  Q,.  If  then  we  multiply 
and  divide  by 


that  is,  by  the  heat  brought  from  the  boiler  by  one  pound  of 
steam,  we  shall  have  in  either  case 

60  X  33QOQ  X  G,  60  X  33000 


778(G,-G,)G,     ~ 
where 

-  _  a  -  a 

~~ 


is  the  efficiency  for  the  cycle. 

Actual  Steam-engine.  —  The  indicator-diagram  from  air 
actual  steam-engine  differs  from  the  cycle  for  a  non-conduct- 
ing engine  in  two  ways:  there  are  losses  of  pressure  between 
the  boiler  and  the  cylinder  and  between  the  cylinder  and  the 
condenser,  due  to  the  resistance  to  the  flow  of  steam  through 
pipes,  valves,  and  passages;  and  there  is  considerable  inter- 
ference of  the  metal  of  the  cylinder  with  the  action  of  the 
steam  in  the  cylinder.  The  losses  of  pressure  may  be  mini- 


242  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

mized  for  a  slow-moving  engine  by  making  the  valves  anc 
passages  direct  and  large.      The  interference  of  the  walls  o 
the  cylinder  cannot  be  prevented,  but  may  be  ameliorated  by 
using  superheated  steam  or  by  steam-jacketing. 

When  steam  enters  the  cylinder  of  an  engine,  some  of  il 
is  condensed  on  the  walls  which  were  cooled  by  contact  with 
exhaust-steam,  thereby  heating  them  up  nearly  to  the  tempera- 
ture of  the  steam.  After  cut-off  the  pressure  of  the  steam  is 
.reduced  by  expansion  and  some  of  the  water  on  the  walls  o 
the  cylinder  vaporizes.  At  release  the  pressure  falls  rapidly 
to  the  back-pressure,  and  the  water  remaining  on  the  walls  is 
nearly  if  not  all  vaporized.  It  is  at  once  evident  that  so  much 
of  the  heat  as  remains  in  the  walls  until  release  and  is  thrown 
out  during  exhaust  is  a  direct  loss;  and  again,  the  heat  which 
is  restored  during  expansion  does  work  with  less  efficiency 
because  it  is  reevaporated  at  less  than  the  temperature  in  the 
boiler  or  in  the  cylinder  during  admission.  A  complete  state- 
ment of  the  action  of  the  walls  of  the  cylinder  of  an  engine 
with  quantitative  results  from  tests  on  engines,  was  first  given 
by  Hirn.  His  analysis  of  engine  tests,  showing  the  inter- 
changes of  heat  between  the  walls  of  the  cylinder  and  the 
steam,  will  be  given  later.  It  is  sufficient  to  know  now  that 
a  failure  to  consider  the  action  of  the  walls  of  the  cylindei 
leads  to  gross  errors,  and  that  an  attempt  to  base  the  design 
of  an  engine  on  the  theory  of  a  steam-engine  with  a  non- 
conducting cylinder  can  lead  only  to  confusion  and  disappoint- 
ment. 

The  most  apparent  effect  of  the  influence  of  the  walls  o 
the  cylinder  on  the  indicator-diagram  is  to  change  the  expan- 
sion and  the  compression  lines;  the  former  exhibits  this 
change  most  clearly.  In  the  first  place  the  fluid  in  the 
cylinder  at  cut-off  consists  of  from  twenty  to  fifty  per  cent 
hot  water,  which  is  found  mainly  adhering  to  the  walls  of  the 
cylinder.  Even  if  there  were  no  action  of  the  walls  during 
expansion  the  curve  would  be  much  less  steep  than  the  adia- 
batic  line  for  drv  saturated  steam.  But  the  reevaooration 


THE  STEAM-ENGINE.  243 

•during  expansion  still  further  changes  the  curve,  so  that  it  is 
usually  less  steep  than  the  rectangular  hyperbola. 

It  may  be  mentioned  that  the  fluctuations  of  temperature 
in  the  walls  of  a  steam-engine  cylinder  caused  by  the  conden- 
sation and  reevaporation  of  water  do  not  extend  far  from  the 
surface,  but  that  at  a  very  moderate  depth  the  temperature 
remains  constant  so  long  as  the  engine  runs  under  constant 
conditions. 

The  performance  of  a  steam-engine  is  commonly  stated  in 
pounds  of  steam  per  horse-power  per  hour.  For  example,  a 
small  Corliss  engine,  developing  16.35  horse-power  when 
running  at  61.5  revolutions  per  minute  under  77.4  pounds 
boiler-pressure,  used  548  pounds  of  steam  in  an  hour.  The 
steam  consumption  was 

548-  16.35  =  33.5 

pounds  per  horse-power  per  hour. 

This  method  was  considered  sufficient  in  the  earlier  his- 
tory of  the  steam-engine,  and  may  now  be  used  for  comparing 
simple  condensing  or  non-condensing  engines  which  use  sat- 
urated steam  and  do  not  have  a  steam-jacket,  for  the  total 
heat  of  steam,  and  consequently  the  cost  of  making  steam 
from  water  at  a  given  temperature  increases  but  slowly  with 
the  pressure. 

The  performance  of  steam-engines  may  be  more  exactly 
stated  in  British  thermal  units  per  horse-power  per  minute. 
This  method,  or  some  method  equivalent  to  it,  is  essential  in 
making  comparisons  to  discover  the  advantages  of  superheat- 
ing, steam-jacketing,  and  compounding.  For  example,  the 
engine  just  referred  to  used  steam  containing  two  per  cent  of 
moisture,  so  that  x^  at  the  steam-pressure  of  77.4  pounds  was 
0.98.  The  barometer  showed  the  pressure  of  the  atmosphere 
to  be  14.7  pounds,  and  this  was  also  the  back-pressure  during 
exhaust.  If  it  be  assumed  that  the  feed-water  was  or  could 
be  heated  to  the  corresponding  temperature  of  212°  F.,  the 


244  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

heat  required  to  evaporate  it  against  77.4  pounds  above  the 
atmosphere  or  92.1  pounds  absolute  was 

*iri  +  ?i  —  <li  =  0.98X888.4+  291.7—  180.8  =  981.5  B.  T.  U. 

The  thermal  units  per  horse-power  per  minute  were 

981.5  x  33-5 


60 


=  548. 


Efficiency  of  the  Actual  Engine.  —  When  the  thermal 
units  per  horse-power  per  minute  are  known  or  can  be  readily 
calculated,  the  efficiency  of  the  actual  steam-engine  may  be 
found  by  the  following  method:  A  horse-power  corresponds 
to  the  development  of  33000  foot-pounds  per  minute,  which 
are  equivalent  to 

33000  -=-  778  =  42.42 

thermal  units.  This  quantity  is  proportional  to  Ql  —  Q9,  and 
the  thermal  units  consumed  per  horse-power  per  minute  are 
proportional  to  Qlt  so  that  the  efficiency  is 

_  6»  -  6,  42.42 


__ 
"         <2i         ~  B.  T.  U.  per  H.P.  per  min." 

For  example,  the  Corliss  engine  mentioned  above  had  an 
efficiency  of 

42.42  ~  548  =0.077. 

This  same  method  may  evidently  be  applied  to  any  heat- 
engine  for  which  the  consumption  in  thermal  units  per  horse- 
power per  hour  can  be  applied. 

From  the  tests  reported  on  page  327  it  appears  that  the 
engine  in  the  laboratory  of  the  Massachusetts  Institute  of 
Technology  on  one  occasion  used  13.73  pounds  of  steam  per 
horse-power  per  hour,  of  which  10.86  pounds  were  supplied 
to  the  cylinders  and  2.87  pounds  were  condensed  in  steam- 


THE   STEAM-ENGINE.  245 

jackets  on  the  cylinders.  The  steam  in  the  supply-pipe  had 
the  pressure  of  157.7  pounds  absolute,  and  contained  1.2  per 
cent  of  moisture.  The  heat  supplied  to  the  cylinders  per 
minute  in  the  steam  admitted  was 

10.86^^  +  q,  -  ?,)  +  60 

=  10.86(0.988  X  858.3  +  334-2  —  126.4)  -*-  60  =  191.1  B.  T.  u.  ; 

q^  being  the  heat  of  the  liquid  at  the  temperature  of  the  back- 
pressure of  4.5  pounds  absolute. 

The  steam  condensed  in  the  steam-jackets  was  withdrawn 
at  the  temperature  due  to  the  pressure  and  could  have  been 
returned  to  the  boiler  at  that  temperature;  consequently  the 
heat  required  to  vaporize  it  was  rlf  and  the  heat  furnished  by 
the  steam  in  the  jackets  was 

2.87  X  0.98  X  858.3  -=-  60  —  40.6  B.  T.  U. 
The  heat  consumed  by  the  engine  was 

191.1  +  40.6  =  231.7  B.  T.  u. 

per  horse-power  per  minute,  and  the  efficiency  was 
rf  —  42.42  ^-  231.7  =  0.183. 

The  efficiency  of  Carnot's  cycle  for  the  range  of  tempera- 
tures corresponding  to  157.7  and  4.  5  pounds  absolute,  namely, 
822°.  9  and  6i8°.4  absolute,  is 


The  efficiency  for  a  non-conducting  engine  with  complete 
expansion,  calculated  by  equation  (255),  is  for  this  case 

„"  =  ,  .       _^^_  _  0.8214  X  1004.2        =  . 

r,+fc-fc  858.3  +  334-2-126.1 


246  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

*  is  calculated  by  the  equation 


858.3  =  a82I 


During  the  test  in  question  the  terminal  pressure  at  the 
end  of  the  expansion  in  the  low-pressure  cylinder  was  6 
pounds  absolute,  which  gives 


and  the  efficiency  by  equation  (260)  was 

fc  —  gc  +  q*  —  A(pc  —  pt  )xcuc 


_  0.8317x995.2- 


858.3  +  334.2-I26.I 

=  0.222. 

The  real  criterion  of  the  perfection  of  the  action  of  an 
engine  is  the  ratio  of  its  actual  efficiency  to  that  of  a  perfect 
engine.  If  for  the  perfect  engine  we  choose  Carnot's  cycle 
the  ratio  is 

w        0.183 

—  =  -  —  = 
rf      0.2485 

But  if  we  take  for  our  standard  an  engine  with  a  cylinder  of 
non-conducting  material  the  ratio  for  complete  expansion  is 

77       0.183 

4,  =  --  -  =  0.807. 

i/'      0.227 


THE   STEAM-ENGINE.  247 

For  incomplete  expansion  the  ratio  is 
rj         0.183 


I/"    ~  0.222 


=  0.824. 


To  complete  the  comparison  it  is  interesting  to  calculate 
the  steam-consumption  for  a  non-conducting  steam-engine  by 
equation  (261),  both  for  complete  and  for  incomplete  expan- 
sion. For  complete  expansion  we  have 

60  X  33000 

=  10.5  pounds. 


778  X  0.227(858.3  +  334.2  —  126.1 
and  for  incomplete  expansion 

60  X  33000 
778  X  0.222(858.3  +  334-2  -HieT)  =    '°-7p0 


per  horse-power  per  hour. 

But  if  these  steam-consumptions  are  compared  with  the 
actual  steam-consumption  of  13.73  pounds  per  horse-power 
per  hour,  the  ratios  are 

10.5  -h  13.73  =  0.766     and      10.7  -h  13.73  —  0.783, 

which  are  very  different  from  the  ratios  of  the  efficiencies. 
The  discrepancy  is  due  to  the  fact  that  more  than  a  fourth  of 
the  steam  used  by  the  actual  engine  is  condensed  in  the 
jackets  and  returned  at  full  steam  temperature  to  the  boiler, 
while  the  non-conducting  engine  has  no  jacket,  but  is  assumed 
to  use  all  the  steam  in  the  cylinder. 

From  this  discussion  it  appears  that  there  is  not  a  wide 
margin  for  improvement  of  a  well-designed  engine  running" 
under  favorable  conditions.  Improved  economy  must  be 
sought  either  by  increasing  the  range  of  temperatures  (raising 
the  steam-pressure  or  improving  the  vacuum),  or  by  choosing 
some  other  form  of  heat-motor,  such  as  the  gas-engine. 

Attention    should    be    called    to    the    fact    that   the    real 


248 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


criterion  of  the  economy  of  a  heat-engine  is  the  cost  of  pro- 
ducing power  by  that  engine.  The  cost  may  be  expressed 
in  thermal  units  per  horse-power  per  minute,  in  pounds  of 
steam  per  horse-power  per  hour,  in  coal  per  horse-power  per 
hour,  or  directly  in  money.  The  expression  in  thermal  units 
is  the  most  exact,  and  the  best  for  comparing  engines  of  the 
slme  class,  such  as  steam-engines.  If  'the  same  fuel  can  be 
used  for  different  engines,  such  as  steam-  and  gas-engines, 
then  the  cost  in  pounds  of  fuel  per  horse-power  per  hour  may 
be  most  instructive.  But  in  any  case  the  money  cost  must 
be  the  final  criterion.  The  reason  why  it  is  not  more  fre- 
quently stated  in  reports  of  tests  is  that  it  is  in  many  cases 
somewhat  difficult  to  determine,  and  because  it  is  affected  by 
market  prices  which  are  subject  to  change. 

At  the  present  time  a  pressure  as  high  as  150  pounds 
above  the  atmosphere  is  used  where  good  economy  is  expected. 
It  appears  from  the  table  on  page  233,  showing  the  efficiency 
of  Carnot's  cycle  for  various  pressures,  that  the  gain  in 
economy  by  increasing  steam-pressure  above  150  pounds  is 
slow.  The  same  thing  is  shown  even  more  clearly  by  the 
following  table: 

EFFECT    OF    RAISING    STEAM-PRESSURE. 


Non-conducting  Engine. 

Probable  Performance,  Actual 
Engine. 

pressure 
by  Gauge. 

Efficiency, 
Carnot's  Cycle. 

Efficiency. 

B.  T.U.  per 
H.P.  per 

B.  T.U.  per 
H.P.  per 

Steam 
per  H.P. 

Minute. 

Minute. 

per  Minute. 

150 

0.302 

0.272 

156 

195 

n-5 

200 

0.320 

0.288 

147 

I84 

10.5 

300 

0-347 

0.306 

135 

169 

9.6 

In  the  calculations  for  this  table  the  steam  is  supposed  to 
be  dry  as  it  enters  the  cylinder  of  the  engine  and  the  back- 
pressure is  supposed  to  be  1.5  pounds  absolute,  while  the 
expansion  for  the  non-conducting  engine  is  assumed  to  be 
complete.  The  heat-consumption  of  the  non-conducting 


THE   STEAM-ENGINE.  249 

engine  is  obtained  by  dividing  42.42   by  the  efficiency;   thus 
for  150  pounds 

42.42  -7-  0.272  =  156. 

The  heat-consumption  of  the  actual  engine  is  assumed  to 
be  one-fourth  greater  than  that  of  the  non-conducting  engine. 
The  steam-consumption  is  calculated  by  the  reversal  of  the 
method  of  calculating  the  thermal  units  per  horse-power  per 
minute  from  the  steam  per  horse-power  per  hour,  and  for 
simplicity  all  of  the  steam  is  assumed  to  be  supplied  to  the 
cylinder.  But  an  engine  which  shall  show  such  an  economy 
for  a  given  pressure  as  that  set  down  in  the  table  must  be  a 
triple  or  a  quadruple  engine  and  must  be  thoroughly  steam- 
jacketed.  The  actual  steam-consumption  is  certain  to  be  a 
little  larger  than  that  given  in  the  table,  as  steam  condensed 
in  a  steam-jacket  yields  less  heat  than  that  passed  through 
the  cylinder. 

It  is  very  doubtful  if  the  gain  in  fluid  efficiency  due  to 
increasing  steam-pressure  above  150  or  200  pounds  is  not 
offset  by  the  greater  friction  and  the  difficulty  of  maintaining 
the  engine.  Higher  pressures  than  200  pounds  are  used  only 
where  great  power  must  be  developed  with  small  weight  and 
space,  as  in  torpedo-boats. 

Condensers. — Two  forms  of  condensers  are  used  to  con- 
dense the  steam  from  a  steam-engine,  known  as  jet-condensers 
and  surface-condensers.  The  former  are  commonly  used  for 
land  engines;  they  consist  of  a  receptacle  having  a  volume 
equal  to  one-fourth  or  one-third  of  that  of  the  cylinder  or 
cylinders  that  exhaust  into  it,  into  which  the  steam  passes 
from  the  exhaust-pipe  and  where  it  meets  and  is  condensed 
by  a  spray  of  cold  water. 

If  it  be  assumed  that  the  steam  in  the  exhaust-pipe  is  dry 
and  saturated  and  that  it  is  condensed  from  the  pressure  p 
and  cooled  to  the  temperature  /*,  then  the  heat  yielded  per 
pound  of  steam  is 


250  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

where  A  is  the  total  heat  of  steam  at  the  pressure  p  and  qk  is 
the  heat  of  the  liquid  at  the  temperature  tk.  The  heat 
acquired  by  each  pound  of  condensing  or  injection  water  is 


where  gi  is  the  heat  of  the  liquid  at  the  temperature  t{  of  the 
injection-water  as  it  enters  the  condenser.  Each  pound  of 
steam  will  require 


pounds  of  injection-water. 

For  example,  steam  at  4  pounds  absolute  has  for  the  total 
heat  1  128.6.  If  the  injection-water  enters  with  a  temperature 
of  60°  F.  and  leaves  with  a  temperature  of  120°  F.,  then 
each  pound  of  steam  will  require 

h^-Jk  _     1128.6  —  88.1  _ 
<77—~ft  ~  '   88.1  —  28.12   : 

pounds  of  injection-water.  This  calculation  is  used  only  to 
aid  in  determining  the  size  of  the  pipes  and  passages  leading 
water  to  and  from  the  condenser,  and  the  dimensions  of  the 
air-pump.  Anything  like  refinement  is  useless  and  impossi- 
ble, as  conditions  are  seldom  well  known  and  are  liable  to  vary. 
From  20  to  30  times  the  weight  of  steam  used  by  the  engine 
is  commonly  taken  for  this  purpose. 

The  jet-condensers  cannot  be  used  at  sea  when  the  boiler- 
pressure  exceeds  40  pounds  by  the  gauge;  all  modern 
steamers  are  consequently  supplied  with  surface-condensers 
which  consist  of  receptacles,  which  are  commonly  rectan- 
gular in  shape,  into  which  steam  is  exhausted,  and  where  it 
is  condensed  on  horizontal  brass  tubes  through  which  cold 
sea-water  is  circulated.  The  condensed  water  is  drained  out 
through  the  air-pump  and  is  returned  to  the  boiler.  Thus 
the  feed-water  is  kept  free  from  salt  and  other  mineral  matter 
that  would  be  pumped  into  the  boiler  if  a  jet-condenser  were 


THE   STEAM-ENGINE.  2$l 

used,  and  if  the  feed-water  were  drawn  from  the  mingled 
water  and  condensed  steam  from  such  a  condenser.  Much 
trouble  is,  however,  experienced  from  oil  used  to  lubricate 
the  cylinder  of  the  engine,  as  it  is  likely  to  be  pumped  into 
the  boilers  with  the  feed-water,  even  though  attempts  are 
made  to  strain  or  filter  it  from  the  water. 

The  water  withdrawn  from  a  surface-condenser  is  likely  to 
have  a  different  temperature  from  the  cooling  water  when  it 
leaves  the  condenser.  If  its  temperature  is  /,,  then  we  have 
instead  of  equation  (261) 


(262) 


for  the  cooling  water  per  pound  of  steam.  The  difference  is 
really  immaterial,  as  it  makes  little  difference  in  the  actual 
value  of  G  for  any  case. 

Cooling  Surface.  —  Experiments  on  the  quantity  of  cool- 
ing surface  required  by  a  surface-condenser  are  few  and  unsat- 
isfactory, and  a  comparison  of  condensers  of  marine  engines 
shows  a  wide  diversity  of  practice.  Seaton  says  that  with 
an  initial  temperature  of  60°,  and  with  120°  for  the  feed- 
water,  a  condensation  of  13  pounds  of  steam  per  square  foot 
per  hour  is  considered  fair  work.  A  new  condenser  in  good 
condition  may  condense  much  more  steam  per  square  foot 
per  hour  than  this,  but  allowance  must  be  made  for  fouling 
and  clogging,  especially  for  vessels  that  make  long  voyages. 

Seaton  also  gives  the  following  table  of  square  feet  of 
cooling  surface  per  indicated  horse-power: 


minal  Pressure, 
er  Square  Inch. 

3O 

Square  Feet 
per  I.  H.  P. 

3 

2O          

2.5 

1C 

2.25 

I2i 

,  2. 

IO          , 

1.8 

8       

1.6 

6 

1.5 

252  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

For  ships  stationed  in  the  tropics,  allow  20  per  cent  more; 
for  ships  which  occasionally  visit  the  tropics,  allow  10  per  cent 
more;  for  ships  constantly  in  a  cold  climate,  10  per  cent  less 
may  be  allowed. 

Designing  Engines. — The  only  question  that  is  properly 
discussed  here  is  the  probable  form  of  the  indicator-diagram, 
which  gives  immediately  the  method  of  finding  the  mean 
effective  pressure  and,  consequently,  the  size  of  the  cylinder 
of  the  engine. 

The  most  reliable  way  of  finding  the  expected  mean 
effective  pressure  in  the  design  of  a  new  engine  is  to  measure 
an  indicator-diagram  from  an  engine  of  the  same  or  similar 
type  and  size,  and  working  under  the  same  conditions. 

As  it  can  hardly  be  expected  that  a  diagram  of  exactly 
the  required  form  will  be  at  hand,  a  diagram  like  Fig.  55  may 
be  drawn,  using  the  proper  cut-off,  com- 
pression, and  clearance.  If  an  indicator- 
diagram  taken  from  an  engine  under  similar 
conditions  is  attainable,  it  may  be  used  to 

—   determine    exponential    equations    for    the 

FIG.  55. 

expansion  and  compression  curves;   usually 

the  exponent  will  be  different  for  the  two  curves,  and  must  be 
determined  separately.  For  ordinary  work  it  is  sufficient  to 
use  the  hyperbola  for  both  curves,  and  to  assume  the  steam 
line  a  and  the  back-pressure  line  c  to  be  parallel  to  the  atmos- 
pheric line,  while  the  lead  of  admission  and  exhaust  may  be 
neglected.  It  is  also  customary  to  assume  a  loss  of  pressure 
of  two  or  more  pounds  between  the  boiler  and  the  engine, 
and  a  back-pressure  of  a  like  amount  above  the  pressure 
in  the  condenser  or  the  pressure  of  the  atmosphere,  as  the 
case  may  be. 

If  the  diagram  is  drawn  to  scale,  the  area  and  mean  effec- 
tive pressure  may  be  found  by  measuring  it;  or,  the  form  of 
the  expansion  and  compression  curves  being  assumed,  the 
areas  under  the  steam  line,  the  expansion  curve,  the  back- 
pressure line,  and  the  compression  curves  may  be  calculated 


THE  STEAM-ENGINE.  2$$ 

separately,  integrating  between  limits  when  necessary,  and 
therefrom  the  resulting  area  of  the  diagram  and  the  mean 
effective  pressure  may  be  determined.  Ordinarily,  the  ex- 
pansion and  compression  curves  are  assumed  to  be  hyperbolae. 
Seaton  *  gives  the  following  multipliers  for  finding  the 
mean  effective  pressure  from  that  calculated  by  the  process 
described : 

MULTIPLIERS  FOR  FINDING  PROBABLE  M.  E.  P.,  SIMPLE  EXPANSIVE  ENGINE. 


(I) 

Special  valve-gear,  o 

r  with  sepai 

•ate  cut-off  valve, 

O  Q4 

(2) 

(3) 

Good  ordinary  valves 
Ordinary  valves  and 
un  jacketed  

,  large  ports 
gears  as  in 

,  engine  jacketed, 
general  practice, 

0.9-0.92 

o  80-0  85 

To  estimate  the  consumption  of  steam,  we  may  calculate 
from  the  pressure  and  volume  at  release  the  weight  of  steam 
then  present  in  the  cylinder,  and  in  a  similar  manner  the 
weight  of  steam  caught  in  the  clearance  space  from  the 
volume  and  pressure  at  compression,  both  under  the  assump- 
tion that  the  steam  is  dry  and  saturated.  The  difference  is 
the  steam  exhausted  per  stroke  under  the  assumption;  but  to 
get  a  fair  estimate  of  the  probable  consumption,  it  is  necessary 
to  add  a  fraction  of  this  amount,  depending  on  the  style  and 
size  of  the  engine  and  on  the  conditions  under  which  it  is  to 
run.  Sufficient  data  for  this  purpose  seldom  exist;  so  it  is 
customary  to  add  to  the  calculated  amount  one-fourth  to  one- 
third  of  itself,  to  get  the  probable  consumption  of  non-con- 
densing engines  of  medium  size. 

PROBLEM. — Required  the  dimensions  of  an  engine  to 
give  100  horse-power;  revolutions,  I2O;  gauge-pressure,  80 
pounds;  cut-off  at  ^  stroke;  release  at  end  of  stroke;  com- 
pression at  TV  stroke,  and  clearance  5  per  cent. 

Assume  the  pressure  during  admission  to  be  78  pounds 
and  during  exhaust  to  be  1.3  pounds  above  the  atmosphere, 
and  assume  hyperbolic  expansion  and  compression. 

*  Manual  of  Marine  Engineering. 


254  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  work  during  expansion  is  (Fig.  55) 
A^«  lo&:!r=  I44(78+I4)(0.333+0.05)  pist.  disp.  log. 


0.333+0.05 
so  that  the  mean  pressure  per  square  inch  during  expansion  is 

0.383  X  92-7  log, 
and  the  mean  effective  pressure  is 

0-333  X  92.7  +  0.383  X  92-7  log,  ^~  "  i6X  0.9 

0-383 

-  o.  1 5  X  16  log,  I   -  ==  49.5  pounds. 

If,  further,  the  stroke  of  the  engine  is  twice  the  diameter, 
then 

—  x  —  X  120  X  2  X  49-5 

100  =  -4 1? ; 

33000 

.•.     d  =  12.8$,        5  =  25.70. 

The  volume  of  the  cylinder  will  be  1.93  cubic  feet,  and  the 
terminal  pressure  will  be  33.8  pounds  absolute.  At  33.8 
pounds  the  density  of  steam  is  0.08234,  and  at  16  pounds  it 
is  0.04067.  The  consumption  of  steam  per  horse-power  per 
hour,  on  the  assumption  of  dry  steam  at  release  and  com- 
pression, will  be 

(0.08234 X  I.Q5  — 0.04067 X 0.15)  1.93 X2X  120X60 _ 

I00  22.3  poun   s. 

If  one-third  of  this  quantity  be  added,  then  the  estimated 
consumption  of  steam  will  be  30  pounds  per  horse-power  per 
hour. 

The  calculated  dimensions  are  stated  in  inches  and 
hundredths,  but  in  practice  the  engine  would  be  made  12  J 
inches  in  diameter  by  25!  inches  stroke;  or  possibly  the 
dimensions  13  by  25  would  be  chosen,  since  they  give  nearly 
the  same  volume. 


CHAPTER   XII. 


COMPOUND    ENGINES. 

A  COMPOUND  engine  has  commonly  two  cylinders,  one  of 
which  is  three  or  four  times  as  large  as  the  other.  Steam 
from  a  boiler  is  admited  to  the  small  cylinder,  and  after  doing 
work  in  that  cylinder  it  is  transferred  to  the  large  cylinder, 
from  which  it  is  exhausted,  after  doing  work  again,  into  a 
condenser  or  against  the  pressure  of  the  atmosphere.  If  we 
assume  that  the  steam  from  the  small  cylinder  is  exhausted 
into  a  large  receiver,  the  back-pressure  in  that  cylinder  and 
the  pressure  during  the  admission  to  the  large  cylinder  will 
be  uniform.  If,  further,  we  assume  that  there  is  no  clearance 
in  either  cylinder,  that  the  back-pressure  in  the  small  cylinder 
and  the  forward  pressure  in  the  large  cylinder  are  the  same, 
and  that  the  expansion  in  the  small  cylinder  reduces  the 
pressure  down  to  the  back-pressure  in  that  cylinder,  the 
diagram  for  the  small  cylinder  will  be  A  BCD,  Fig.  52,  and 


FIG.  56.  FIG.  57. 

for  the  large  cylinder  DCFG.  The  volume  in  the  large 
cylinder  at  cut-off  is  equal  to  the  total  volume  of  the  small 
cylinder,  since  the  large  cylinder  takes  from  the  receiver  the 
same  weight  of  steam  that  is  exhausted  by  the  small  cylinder, 
and,  in  this  case,  at  the  same  pressure. 

The    case    just    discussed    is    one    extreme.      The    other 

255 


256  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

extreme  occurs  when  the  small  cylinder  exhausts  directly  into 
the  large  cylinder  without  an  intermediate  receiver.  In  such 
engines  the  pistons  must  begin  and  end  their  strokes  together. 
They  may  both  act  on  the  beam  of  a  beam  engine,  or  they 
may  act  on  one  crank  or  on  two  cranks  opposite  each  other. 

For  such  an  engine,  ABCD,  Fig.  57,  is  the  diagram  for 
the  small  cylinder.  The  steam  line  and  expansion  line  AB 
and  BC  are  like  those  of  a  simple  engine.  When  the  piston 
of  the  small  cylinder  begins  the  return  stroke,  communication 
is  opened  with  the  large  cylinder,  and  the  steam  passes  from 
one  to  the  other,  and  expands  to  the  amount  of  the  difference 
of  the  volume,  it  being  assumed  that  the  communication 
remains  open  to  the  end  of  the  stroke.  The  back-pressure 
line  CD  for  the  small  cylinder,  and  the  admission  line  HI  for 
the  large  cylinder,  gradually  fall  on  account  of  this  expansion. 
The  diagram  for  the  large  cylinder  is  HIKG,  which  is  turned 
toward  the  left  for  convenience. 

To  combine  the  two  diagrams,  draw  the  line  abed,  parallel 
to  V'OV,  and  from  b  lay  off  bd  equal  to  ca\  then  d  is  one 
point  of  the  expansion  curve  of  the  combined  diagram.  The 
point  C  corresponds  with  //,  and  £,  corresponding  with  /,  is 
as  far  to  the  right  as  /  is  to  the  left.  ^ 

For  a  non-conducting  cylinder,  the  combined  diagram  for 
a  compound  engine,  whether  with  or  without  a  receiver,  is 
the  same  as  that  for  a  simple  engine  which  has  a  cylinder  the 
same  size  as  the  large  cylinder  of  the  compound  engine,  and 
which  takes  at  each  stroke  the  same  volume  of  steam  as  the 
small  cylinder,  and  at  the  same  pressure.  The  only  advan- 
tage gained  by  the  addition  of  the  small  cylinder  to  such  an 
engine  is  a  more  even  distribution  of  work  during  the  stroke, 
and  a  smaller  initial  stress  on  the  crank-pin. 

Compound  engines  may  be  divided  into  two  classes — those 
with  a  receiver  and  those  without  a  receiver;  the  latter  are 
called  "  Woolf  engines"  on  the  continent  of  Europe.  En- 
gines without  a  receiver  must  have  the  pistons  begin  and  end 
their  strokes  at  the  same  time;  they  may  act  on  the  same 


COMPOUND   ENGINES. 

crank  or  on  cranks  180°  apart.  The  pistons  of  a  receiver 
compound  engine  may  make  strokes  in  any  order.  A  form 
of  receiver  compound  engine  with  two  cylinders,  commonly 
used  in  marine  work,  has  the  cranks  at  90°  to  give  handiness 
and  certainty  of  action.  Large  marine  engines  have  been 
made  with  one  small  cylinder  and  two  large  or  low-pressure 
cylinders,  both  of  which  draw  steam  from  the  receiver  and 
exhaust  to  the  condenser.  Such  engines  usually  have  the 
cranks  at  120°,  though  other  arrangements  have  been  made. 

Nearly  all  compound  engines  have  a  receiver,  or  a  space 
between  the  cylinders  corresponding  to  one,  and  in  no  case  is 
the  receiver  of  sufficient  size  to  entirely  prevent  fluctuations  of 
pressure.  In  the  later  marine  work  the  receiver  has  been 
made  small,  and  frequently  the  steam-chests  and  connecting 
pipes  have  been  allowed  to  fulfil  that  function.  This  contrac- 
tion of  size  involves  greater  fluctuations  of  pressure,  but  for 
other  reasons  it  appears  to  be  favorable  to  economy. 

Under  proper  conditions  there  is  a  gain  from  using  a  com- 
pound engine  instead  of  a  simple  engine,  which  may  amount 
to  ten  per  cent  or  more.  This  gain  is  to  be  attributed  to  the 
division  of  the  change  of  temperature  from  that  of  the  steam  at 
admission  to  that  of  exhaust  into  two  stages,  so  that  there  is- 
less  fluctuation  of  temperature  in  a  cylinder  and  consequently 
less  interchange  of  heat  between  the  steam  and  the  walls  of 
the  cylinder. 

Compound  Engine  without  Receiver. — The    indicator- 
diagrams    from    a    compound    engine  without  a  receiver  are 
represented  by  Fig.  58.      The  steam  line  and 
expansion  line  of  the  small  cylinder,  AB  and 
BC,    do    not   differ   from   those  of   a   simple 
engine.      At   C  the  exhaust  opens,   and   the 
steam  suddenly  expands  into  the  space  be- 
tween the  cylinders  and  the  clearance  of  the  L 
large   cylinder,  and   the   pressure   falls   from 
C  to  D.      During  the  return  stroke  the  volume  in  the  large 
cylinder  increases  more  rapidly  than  that  of  the  small  cylinder 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


decreases,  so  that  the  back-pressure  line  DE  gradually  falls, 
as  does  also  the  admission  line  HI  of  the  large  cylinder,  the 
difference  between  these  two  lines  being  due  to  the  resistance 
to  the  flow  of  steam  from  one  to  the  other.  At  E  the  com- 
munication between  the  two  cylinders  is  closed  by  the  cut-off 
of  the  large  cylinder;  the  steam  is  then  compressed  in  the 
small  cylinder  and  the  space  between  the  two  cylinders  to  F, 
at  which  the  exhaust  of  the  small  cylinder  closes;  and  the 
remainder  of  the  diagram  FGA  is  like  that  of  a  simple  engine. 
Prom  /,  the  point  of  cut-off  of  the  large  cylinder,  the 
remainder  of  the  diagram  IKLMNH  is  like  the  same  part  of 
the  diagram  of  a  simple  engine. 

The  difference  between  the  lines  ED  and  HI  and  the 
"  drop  "  CD  at  the  end  of  the  stroke  of  the  small  piston  indi- 
cate waste  or  losses  of  efficiency.  The  compression  EFG  and 
the  accompanying  independent  expansion  IK  in  the  large 
cylinder  show  a  loss  of  power  when  compared  with  a  diagram 
like  Fig.  56  for  an  engine  which  has  no  clearance  or  inter- 
mediate space;  but  compression  is  required  to  fill  waste 
spaces  with  steam.  The  compression  EF  is  required  to 
reduce  the  drop  CD,  and  the  compression  FG  fills  the  clear- 
ance in  anticipation  of  the  next  supply  from  the  boiler. 

Neither  compression  is  complete 
in  Fig.  58. 

Diagrams  from  a  pumping  en- 
gine at  Lawrence,  Massachusetts, 
are  shown  by  Fig.  59.  The 
rounding  of  corners  due  to  the 
indicator  make  it  difficult  to  de- 
termine the  location  of  points  like 
Z>,  E,  F,  and  /on  Fig.  58.  The 
low-pressure  diagram  is  taken 
with  a  weak  spring,  and  so  has  an 
FlG-  59-  exaggerated  height. 

Compound  Engine  with  Receiver. — It  has  already  been 
pointed  out  that  some  receiver  space  is  required  if  the  cranks 


COMPOUND    ENGINES.  259 

of  a  compound  engine  are  to  be  placed  at  right  angles. 
When  the  receiver  space  is  small,  as  on  most  marine  engines, 
the  fluctuations  of  pressure  in  the 
receiver  are  very  notable.  This  is 
exhibited  by  the  diagrams  in  Fig.  60, 
which  were  taken  from  a  yacht  engine. 
An  intelligent  conception  of  the 
causes  and  meaning  of  such  fluctuations 

can  be  best  obtained  by  constructing    ^ J~ 

ideal  diagrams  for  special  cases,  as  ex-  FIG.  60. 

plained  on  page  269. 

Triple  and  Quadruple  Compound  Engines. — The  same 
influences  which  introduced  the  compound  engines,  when  the 
common  steam-pressure  changed  from  forty  to  eighty  pounds 
to  the  square  inch,  have  brought  in  the  successive  expansion 
through  three  cylinders  (the  high-pressure,  intermediate,  and 
low-pressure  cylinders)  now  that  125  to  170  pounds  pressure 
are  employed.  Just  as  three  or  more  cylinders  are  combined 
in  various  ways  for  compound  engines,  so  four,  five,  or  six 
cylinders  have  been  arranged  in  various  manners  for  triple- 
expansion  engines;  for  example,  a  compound  engine  with 
two  cylinders  may  be  conveniently  changed  into  a  triple-ex- 
pansion engine  by  the  addition  of  a  small  high-pressure  cylin- 
der over  each  of  the  existing  cylinders. 

Quadruple  engines  with  four  successive  expansions  have 
been  employed  with  high-pressure  steam,  but  with  the  advis- 
able pressures  for  present  use  the  extra  complication  and  fric- 
tion make  it  a  doubtful  expedient. 

Total  Expansion. — In  Figs.  56  and  57,  representing  the 
diagrams  for  compound  engines  without  clearance  and  without 
drop  between  the  cylinders,  the  total  expansion  is  the  ratio 
of  the  volumes  at  E  and  at  A  ;  that  is,  of  the  low-pressure 
piston  displacement  to  the  displacement  developed  by  the 
high-pressure  piston  at  cut-off.  The  same  ratio  is  called  the 
total  or  equivalent  expansion  for  any  compound  engine, 
though  it  may  have  both  clearance  and  drop.  Such  a  con- 


200  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

ventional  total  expansion  is  commonly  given  for  compound 
and  multiple-expansion  engines,  and  is  a  convenience  because 
it  is  roughly  equal  to  the  ratio  of  the  initial  and  terminal 
pressures;  that  is,  of  the  pressure  at  cut-off  in  the  high- 
pressure  cylinder  and  at  release  in  the  low-pressure  cylinder. 
It  has  no  real  significance,  and  is  not  equivalent  of  the  expan- 
sion in  the  cylinder  of  a  simple  engine,  by  which  we  mean 
the  ratio  of  the  volume  at  release  to  that  at  cut-off,  taking 
account  of  clearance.  And  further,  since  the  clearance  of  the 
high-  and  the  low-pressure  cylinders  are  different  there  can 
be  no  real  equivalent  expansion. 

If  the  ratio  of  the  cylinders  is  R  and  the  cut-off  of  the 

high-pressure  cylinder  is  at  —  of  the  stroke,  then  the  total 
expansion  is  represented  by 

E  =  eR (263) 

and 

l-  =  R  +  E (264) 

This  last  equation  is  useful  in  determining  approximately  the 
cut-off  of  the  high-pressure  cylinder. 

For  example,  if  the  initial  pressure  is  100  pounds  absolute 
and  the  terminal  pressure  is  to  be  10  pounds  absolute,  then 
the  total  expansions  will  be  about  10.  If  the  ratio  of  the 
cylinders  is  3^,  then  the  high-pressure  cut-off  will  be  about 

-f  =  3*  -*-  10  =  0.35 

of  the  stroke. 

Low-pressure  Cut-off. — The  cut-off  of  the  low-pressure 
cylinders  in  Figs.  56  and  57  is  controlled  by  the  ratio  of  the 
cylinders,  since  the  volumes  in  the  low-pressure  cylinder  at 
cut-off  is  in  each  case  made  equal  to  the  high-pressure  piston 
displacement;  this  is  done  to  avoid  a  drop.  If  the  cut-off 


COMPOUND   ENGINES.  261 

were  lengthened  there  would  be  a  loss  of  pressure  or  drop  at 

the  end  of  the  stroke  of  the  high-pressure  piston,  as  is  shown 

by  Fig.    61,    for  an   engine   with   a 

large    receiver    and    no     clearance. 

Such  a  drop  will  have  some  effect  on 

the  character  of  the  expansion  line 

C" E  of  the  low-pressure    cylinder, 

both  for  a  non-conducting  and  for 

the  actual  engine  with  or  without  a 

clearance.      Its  principal  effect  will, 

however,   be  on  the  distribution  of 

FIG.  61. 
work  between  the   cylinders;    for  it 

is  evident  that  if  the  cut-off  of  the  low-pressure  cylinder  is 
shortened  the  pressure  at  C"  will  be  increased  because  the 
same  weight  of  steam  is  taken  in  a  smaller  volume.  The 
back-pressure  DC'  of  the  high-pressure  cylinder  will  be  raised 
and  the  work  will  be  diminished;  while  the  forward  pressure 
DC"  of  the  low-pressure  cylinder  will  be  raised,  increasing  the 
work  in  that  cylinder. 

Ratio  of  Cylinders. — In  designing  compound  engines, 
more  especially  for  marine  work,  it  is  deemed  important  for 
the  smooth  action  of  the  engine  that  the  total  work  shall  be 
evenly  distributed  upon  the  several  cranks  of  the  engines,  and 
that  the  maximum  pressure  on  each  of  the  cranks  shall  be  the 
same,  and  shall  not  be  excessive.  In  case  two  or  more  pis- 
tons act  on  one  crank,  the  total  work  and  the  resultant 
pressure  on  those  pistons  are  to  be  considered;  but  more 
commonly  each  piston  acts  on  a  separate  crank,  and  then  the 
work  and  pressure  on  the  several  pistons  are  to  be  considered. 

In  practice  both  the  ratio  of  the  cylinders  and  the  total 
expansions  are  assumed,  and  then  the  distribution  of  work 
and  the  maximum  loads  on  the  crank-pins  are  calculated, 
allowing  for  clearance  and  compression.  Designers  of  engines 
usually  have  a  sufficient  number  of  good  examples  at  hand  to 
enable  them  to  assume  these  data.  In  default  of  such  data 
it  may  be  necessary  to  assume  proportions,  to  make  prelimi- 


262  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

nary  calculations,  and  to  revise  the  proportions  till  satisfactory 
results  are  obtained.  For  compound  engines  using  80  pounds 
steam-pressure  the  ratio  is  I  :  3  or  I  :  4.  For  triple-ex- 
pansion engines  the  cylinders  may  be  made  to  increase  in 
the  ratio  I  :  2  or  I  :  2j. 

Approximate  Indicator-diagrams. — The  indicator-dia- 
grams from  some  compound  and  multiple-expansion  engines 
are  irregular  and  apparently  erratic,  depending  on  the 
sequence  of  the  cranks,  the  action  of  the  valves,  and  the 
relative  volumes  of  the  cylinders  and  the  receiver  spaces.  A 
good  idea  of  the  effects  and  relations  of  these  several  influ- 
ences can  be  obtained  by  making  approximate  calculations  of 
pressures  at  the  proper  parts  of  the  diagrams  by  a  method 
which  will  now  be  illustrated. 

For  such  a  calculation  it  will  be  assumed  that  all  expan- 
sion lines  are  rectangular  hyperbolae,  and  in  general  that  any 
change  of  volume  will  cause  the  pressure  to  change  inversely 
as  the  volume.  Further,  it  will  be  assumed  that  when  com- 
munication is  opened  between  two  volumes  where  the  pres- 
sures are  different,  the  resultant  pressure  may  be  calculated 
by  adding  together  the  products  of  each  volume  by  its 
pressure,  and  dividing  by  the  sum  of  the  volumes.  Thus  if 
the  pressure  in  a  cylinder  having  the  volume  vc  is  pc1  and  if 
the  pressure  is  pr  in  a  receiver  where  the  volume  is  vv,  then 
after  the  valve  opens  communication  from  the  cylinder  to  the 
receiver  the  pressure  will  be 

4—PcVc+PrVr 

Vc  +  Vr      ' 

The  same  method  will  be  used  when  three  volumes  are  put 
into  communication. 

It  will  be  assumed  that  there  are  no  losses  of  pressure  due 
to  throttling  or  wire-drawing;  thus  the  steam  line  for  the 
high-pressure  cylinder  will  be  drawn  at  the  full  boiler-pressure, 
and  the  back-pressure  line  in  the  low-pressure  cylinder  will  be 
drawn  to  correspond  with  the  vacuum  in  the  condenser. 


COMPOUND    ENGINES. 


263 


Again,  cylinders  and  receiver  spaces  in  communication  will  be 
assumed  to  have  the  same  pressure. 

For  sake  of  simplicity  the  motions  of  pistons  will  be 
assumed  to  be  harmonic. 

Diagrams  constructed  in  this  way  will  never  be  realized  in 
any  engine;  the  degree  of  discrepancy  will  depend  on  the 
type  of  engine  and  the  speed  of  rotation.  For  slow-speed 
pumping-engines  the  discrepancy  is  small  and  all  irregularities 
are  easily  accounted  for.  On  the  other  hand  the  discrepancies 
are  large  for  high-speed  marine-engines,  and  for  compound 
locomotives  they  almost  prevent  the  recognition  of  the  events 
of  the  stroke. 

Direct-expansion  Engine. — If  the  two  pistons  of  a  com- 
pound engine  move  together  or  in  opposite  directions  the 
diagrams  are  like  those  shown  by  Fig.  62.  Steam  is  admitted 
to  the  high-pressure  cylinder  from  a  to  b;  cut-off  occurs  at  b, 
and  be  represents  expansion  to  the  end  of  the  stroke ;  be  being 
a  rectangular  hyperbola  referred  to  the  axis  OV  and  OP,  from 
which  #,  b,  and  c  are  laid  off  to  represent  absolute  pressures 
and  volumes,  including  clearance. 

p    P 


FIG.  62. 

At  the  end  of  the  stroke  release  from  the  high-pressure 
cylinder  and  admission  to  the  low-pressure  cylinder  are 
assumed  to  take  place,  so  that  communication  is  opened  from 
the  high-pressure  cylinder  through  the  receiver  space  into 
the  low-pressure  cylinder.  As  a  consequence  the  pressure 
falls  from  c  to  d,  and  rises  from  n  to  h  in  the  low-pressure 
cylinder.  The  line  O'P'  is  drawn  at  a  distance  from  OP, 


1HK 

UNIVERSITY 


264  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

which  corresponds  to  the  volume  of  the  receiver  space,  and 
the  low-pressure  diagram  is  referred  to  O'P'  and  O'V  as  axes. 

The  communication  between  the  cylinders  is  maintained 
until  cut-off  occurs  at  i  for  the  low-pressure  cylinder.  The 
lines  de  and  hi  represent  the  transfer  of  steam  from  the  high- 
pressure  to  the  low-pressure  cylinder,  together  with  the 
expansion  due  to  the  increased  size  of  the  large  cylinder. 
After  the  cut-off  at  z,  the  large  cylinder  is  shut  off  from  the 
receiver  and  the  steam  in  it  expands  to  the  end  of  the  stroke. 
'The  back-pressure  and  compression  lines  for  that  cylinder  are 
•not  affected  by  compounding,  and  are  like  those  of  a  simple 
•engine.  Meanwhile  the  small  piston  compresses  steam  into 
the  receiver,  as  represented  by  ef,  till  compression  occurs, 
after  which  compression  into  the  clearance  space  is  represented 
by  fg.  The  expansion  and  compression  lines  ik  and  mn  are 
-drawn  as  hyperbolae  referred  to  the  axis  O'P'  and  O'V. 
The  compression  line  ef  is  drawn  as  an  hyperbola  referred  to 
<9'Fand  O'P,  while  fg  is  referred  to  <9Fand  OP. 

In  Fig.  62  the  two  diagrams  are  drawn  with  the  same  scale 
for  volume  and  pressure,  and  are  placed  so  as  to  show  to  the 
eye  the  relations  of  the  diagrams  to  each  other.  Diagrams 
taken  from  such  an  engine  resemble  Figs.  59,  which  have  the 
same  length,  and  different  vertical  scales  depending  on  the 
springs  used  in  the  indicators. 

Some  engines  have  only  one  valve  to  give  release  and 
compression  for  the  high-pressure  cylinder  and  admission  and 
•cut-off  for  the  low-pressure  cylinder.  In  such  case  there  is 
no  receiver  space,  and  the  points  e  and /coincide. 

When  the  receiver  is  closed  by  the  compression  of  the 
high-pressure  cylinder  it  is  filled  with  steam  with  the  pressure 
represented  by  f.  It  is  assumed  that  the  pressure  in  the 
receiver  remains  unchanged  till  the  receiver  is  opened  at  the 
end  of  the  stroke.  It  is  evident  that  the  drop  cd  may  be 
reduced  by  shortening  the  cut-off  of  the  low-pressure  cylinder 
so  as  to  give  more  compression  from  e  to /and  consequently 
a  higher  pressure  at /when  the  receiver  is  closed. 


COMPOUND   ENGINES.  26$ 

Representing  the  pressure  and  volume  at  the  several  points 
by/  and  v  with  appropriate  subscript  letters,  and  represent- 
ing the  volume  of  the  receiver  by  vrj  we  have  the  following 
equations: 

pa  =  pb  =  initial  pressure  ; 

pl  =  pm  =  back-pressure  ; 

A  =  P&b  +  vc  I 

A  =  A.^«  •+•  vn ; 

pd=Ph  =  (pcvc  +PnV*  +p/vr)  -r-  (vc  +  vn  +  vr)  ; 

A    =  A  =  Afa:  +  V»  +  Vr}  -5-   (V.  +  Vi  +  V^  J 
Pf   =  Pe(Ve  +  Vr)    +    tyf  +  «V)  J 

A  =A«v -*-**; 

A  =  /»^  -^  v*- 

The  pressures  /c  and  /w  can  be  calculated  directly.  Then 
the  equations  for  pd1  pe,  and  p  form  a  set  of  three  simulta- 
neous equations  with  three  unknown  quantities,  which  can  be 
easily  solved.  Finally,  pe  and  pk  may  be  calculated  directly. 

For  example )  let  us  find  the  approximate  diagram  for  a 
direct-expansion  engine  which  has  the  low-pressure  piston 
displacement  equal  to  three  times  the  high-pressure  piston 
displacement.  Assume  that  the  receiver  space  is  half  the 
smaller  piston  displacement,  and  that  the  clearance  for  each 
cylinder  is  one-tenth  of  the  corresponding  piston  displace- 
ment. Let  the  cut-off  for  each  cylinder  be  at  half-stroke, 
and  the  compression  at  nine-tenths  of  the  stroke;  let  the 
admission  and  release  be  at  the  end  of  the  stroke.  Let  the 
initial  pressure  be  65.3  pounds  by  the  gauge  or  80  pounds 
absolute,  and  let  the  back-pressure  be  two  pounds  absolute. 

If  the  volume  of  the  high-pressure  piston  displacement  be 
taken  as  unity,  then  the  several  required  volumes  are: 

^  —  0.5  +  o.i  =  0.6  vh  =  vn  —  3  x  o.i  =  0.3 

vc  =  vd  —  i.o  +  o.i  =  i.i  vt  =  3(0.5  +  o.i)  =  1.8 

ve  =  0.5  +  o.i  =  0.6  vk  =  vi  =  3(1.0  +  o.i)  —  3.3 

vf  =  o.i  +  o.i  =  0.2  vm=  3(0.1  +  o.i)  —  0.6 

vf=  o.i  vr  —  0.5 


266  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  pressures  may  be  calculated  as  follows: 
A=A  =  8o;        pl=pm=  2; 

PC  =  PbVb  -r-  ^  =  80  X  0.6  -f-  i.i  =  43.6 ; 
A.  =  PmVm  -r-  ^  =  2  X  0.6  -r-  0.3  =  4 ; 

A  =  Afc  +  "«  +  «V)  t  (*.  +  *>i  +  *V)  =  AO-i  +  0.3  +  0.5) 
-  (0.6+  1.8 +0.5)  =  0.65  5^; 

A    =  Afa  +  O   -*•   (*/  +  *V)    =  A(0.6  +  0-5)  *   (0-2  +  0.5) 

=  i-57A=i-57X  0.655^,=  1.034,; 

A  =  (PcVc  +pnVn  +pfvr}  -5-  (ve  +  vn  +  vr] 

=  (80  X  0.6  +  4  X  0.3  +  o.5/y)  -=-0.6  +  0.3  +0.5 
=  25.89 +  o.26/y; 

•/„  =  25.89  +  0.26  x  I.OSA  ;      A*  =  35-36 ; 
A  =  A-  =  0.655^  =  0.655  x  35-36  =  23.2 ; 
pf  =  i.o3A  =  1-03  x  35-36  =  36.5 ; 
A  =//*'/+- ^  =  36.5  X  0.2 -=-0.1  ^=73; 

/^    =/f.t/,.  -r-  Vh  —  23.2   X    1.8  -T-  3.3  =    12.6. 

As  the  pressures  and  volumes  are  now  known  the  diagrams 
of  Fig.  62  may  be  drawn  to  scale.  Or,  if  preferred,  diagrams 
like  Fig.  59  may  be  drawn,  making  them  of  the  same  length 
and  using  convenient  vertical  scales  of  pressure.  If  the 
engine  runs  slowly  and  has  abundant  valves  and  passages  the 
diagrams  thus  obtained  will  be  very  nearly  like  those  taken 
from  the  engine  by  indicators.  If  losses  of  pressure  in  valves 
and  passages  are  allowed  for,  a  closer  approximation  can  be 
made. 

The  mean  effective  pressures  of  the  diagrams  may  be 
readily  obtained  by  the  aid  of  planimeters,  and  may  be  used 
for  estimating  the  power  of  the  engine.  For  this  purpose  we 
should  either  use  the  modified  diagrams  allowing  for  losses  of 
pressure,  or  we  should  affect  the  mean  effective  pressures  by 
a  multiplier  obtained  by  comparison  of  the  approximate  with 
the  actual  diagrams  from  engines  of  the  same  type.  For  a 
slow-speed  pumping-engine  the  multiplier  may  be  as  lai  je  as 
0.9  or  even  more;  for  high-speed  engines  it  may  be  as  small 
as  0.6. 


COMPOUND   ENGINES.  267 

The  mean  effective  pressure  of  the  diagrams  may  be  cal- 
culated from  the  volumes  and  pressures  if  desired,  assuming, 
of  course,  that  the  several  expansion  and  compression  curves 
are  hyperbolae.  The  process  can  be  best  explained  by  apply- 
ing it  to  the  example  already  considered.  Begin  by  finding 
the  mean  pressure  during  the  transfer  of  steam  from  the  high- 
pressure  cylinder  to  the  low-pressure  cylinder  as  represented 
by  de  and  hi.  The  net  effective  work  during  the  transfer  is 

C  v  v  +  v--\-  v 

I  pdv  =  ptvt  log,  -'  =  \^pd(vd  +  vk  +  v^  log,  J 


. 
=  =  144  X  35-4(1.1  +0.3  +0.5)  log,  - 


=  4120  foot-pounds 

for  each  cubic  foot  of  displacement  of  the  high-pressure  piston. 
This  corresponds  with  our  previous  assumption  of  unity  for 
the  displacement  of  that  piston.  The  increase  of  volume  is 

v.+Vf+Vr-fyd  +v*+«v)=o.6+i.8+o.5—  (i.  1+0.3+0.5)=!  ; 
so  that  the  mean  pressure  during  the  transfer  is 
4120  -T-  I  X  144  =  28.6  =  px 

pounds  per  square  inch,  which  acts  on  both  the  high-  and  the 
low-pressure  pistons. 

The  effective  work  for  the  small  cylinder  is  obtained  by 
adding  the  works  under  ab  and  be  and  subtracting  the  works 
under  de,  ef,  and  fg.  So  that 


(  Vc 

=   144   )  Pa(v     —  Va)  +  pbVb  log«  -- 


Vg  -4-  Vr-  Vf 

+  Vr)  loge  —  +  --  p    Vf  \Oge    - 
Vf  -\-  Vr  Vg 

=  144  \  80(0.6  —  o.i)  -|-  80  X  0.6  log,—  —  28.6(1.1  -  0.6) 
(  0.6 

o.  6  -I-  0.5  o.  2  ) 

-   23.2(0.6  +  0.5)  log,  -          --  36.5   X  0.2  log*  - 

0.2  +  0.5  o.i  } 

=  144  X  33.26  =  4789  foot-pounds. 


268  THERMODYNAMICS  OF   THE   STEAM-EA7GIATE. 

This  is  the  work  for  each  cubic  foot  of  the  high-pressure 
piston  displacement,  and  the  mean  effective  pressure  on  the 
small  piston  is  evidently  33.26  pounds  per  square  inch. 

In  a  like  manner  the  work  of  the  large  piston  is 

IV L  =  I44-!  px(Vi  —  Vh)  -\-piVi  loge pl(vi  —  Vm}  —  pmVm  loge  —  [ 

Vi  Vn  ) 

=  144  \  28.6(1.8  -  0.3)  +  23.2  X  1.8  log,  ^f- 
(  I.o 

—  2(3.3  —  0.6)—  2  X  0.6  loge  —  I  —  144  X  61.92  ==  8916  foot-pounds. 

Since  the  ratio  of  the  piston  displacements  is  3,  the  work 
for  each  cubic  foot  of  the  low-pressure  piston  displacement  is 
one-third  of  the  work  just  calculated;  and  the  mean  effective 
pressure  on  the  large  piston  is 

61.92  -r-  3  =  20.64 

pounds  per  square  inch. 

The  proportions  given  in  the  example  lead  to  a  very 
uneven  distribution  of  work;  that  of  the  large  cylinder  being 
nearly  twice  as  much  as  is  developed  in  the  small  cylinder. 
The  distribution  can  be  improved  by  shortening  the  cut-off 
of  the  small  cylinder,  or  lengthening  that  of  the  large 
cylinder,  or  by  increasing  the  size  of  the  large  cylinder. 

As  has  already  been  pointed  out,  the  works  just  calculated 
and  the  corresponding  mean  effective  pressures  are  in  excess 
of  those  that  will  be  actually  developed,  and  must  be  affected 
by  multipliers  which  may  vary  from  0.6  to  0.9,  depending  on 
the  type  and  speed  of  the  engine. 

Cross-compound  Engine. — A  two-cylinder  compound 
engine  with  pistons  connected  to  cranks  at  right  angles  with 
each  other  is  frequently  called  a  cross-compound  engine. 
Unless  a  large  receiver  is  placed  between  the  cylinders  the 
pressure  in  the  space  between  the  cylinders  will  vary  widely. 

Two  cases  arise  in  the  discussion  of  this  engine  according 
as  the  cut-off  of  the  large  cylinder  is  earlier  or  later  than  half- 


COMPOUND    ENGINES. 


269 


stroke;  in  the  latter  case  there  is  a  species  of  double  admission 
to  the  low-pressure  cylinder,  as  is  shown  in  Fig.  63.  For 
sake  of  simplicity  the  release,  and  also  the  admission  for  each 
cylinder,  is  assumed  to  be  at  the  end  of  the  stroke.  If  the 
release  is  early  the  double  admission  occurs  before  half-stroke. 
The  admission  and  expansion  of  steam  for  the  high- 
pressure  cylinder  are  represented  by  ab  and  be.  At  c  release 
occurs,  putting  the  small  cylinder  in  communication  with  the 
intermediate  receiver,  which  is  then  open  to  the  large  cylinder. 


FIG.  03. 

There  is  a  drop  at  cd  and  a  corresponding  rise  of  pressure  mn 
on  the  large  piston,  which  is  then  at  half-stroke;  it  will  be 
assumed  that  the  pressures  at  d  and  at  n  are  identical.  From 
d  to  e  the  steam  is  transferred  from  the  small  to  the  large 
cylinder,  and  the  pressure  falls  because  the  volume  increases; 
no  is  the  corresponding  line  on  the  low-pressure  diagram. 
The  cut-off  at  o  for  the  large  cylinder  interrupts  this  transfer, 
and  steam  is  then  compressed  by  the  small  piston  into  the 
intermediate  receiver  with  a  rise  of  pressure  as  represented 
by  ef.  The  admission  to  the  large  cylinder,  tk>  occurs  when 
the  small  piston  is  at  the  middle  of  its  stroke,  and  causes  a 
drop,  fgj  in  the  small  cylinder.  From  g  to  h  steam  is  trans- 
ferred through  the  receiver  from  the  small  to  the  large 
cylinder.  The  pressure  rises  at  first  because  the  small  piston 
moves  rapidly  while  the  large  one  moves  slowly  until  its  crank 
gets  away  from  the  dead-point ;  afterwards  the  pressure  falls. 
The  line  kl  represents  this  action  on  the  low-pressure  diagram. 
At  h  compression  occurs  for  the  small  cylinder,  and  hi  shows 


2/0  THERMODYNAMICS  OF   7" HE   STEAM-ENGINE. 

the  rise  of  pressure  due  to  compression.  For  the  large 
cylinder  the  line  Im  represents  the  supply  of  steam  from  the 
receiver,  with  falling  pressure  which  lasts  till  the  double 
.admission  at  mn  occurs. 

The  expansion,  release,  exhaust,  and  compression  in  the 
large  cylinder  are  not  affected  by  compounding. 

Strictly,  the  two  parts  of  the  diagram  for  the  low-pressure 
cylinder,  mnopq  and  stklm  belong  to  opposite  ends  of  the 
cylinder,  one  belonging  to  the  head  end  and  one  to  the  crank 
end.  With  harmonic  motion  the  diagrams  from  the  two  ends 
are  identical,  and  no  confusion  need  arise  from  our  neglect  to 
determine  which  end  of  the  large  cylinder  we  are  dealing  with 
at  any  time.  Such  an  analysis  for  the  two  ends  of  the 
cylinder,  taking  account  of  the  irregularity  due  to  the  action 
of  the  connecting-rod,  would  lead  to  a  complexity  that  would 
be  unprofitable. 

A  ready  way  of  finding  corresponding  positions   of  two 
pistons  connected  to  cranks  at  right  angles  with  each  other  is 
by  aid  of  the  diagram  of  Fig.  60.      Let 
O  be  the  centre  of  the  crank-shaft  and 
pRyRxq    be    the    path   of 'the   crank-pin. 
When  one  piston  has  the  displacement  py 
and  its  crank  is  at  ORy,  the  other  crank 
may  be  90°  ahead  at  ORX  and  the  corre- 
FIG   64  spending  piston  displacement  will  be/^r. 

The   same   construction  may   be  used   if 

the  crank  is  90°  'behind  or  if  the  angle  RyORx  is  other  than  a 
right  angle.  The  actual  piston  position  and  crank  angles 
when  affected  by  the  irregularity  due  to  the  connecting-rod 
will  differ  from  those  found  by  this  method,  but  the  position 
found  by  such  a  diagram  wilt  represent  the  average  positions 
very  nearly. 

The  several  pressures  may  be  found  as  follows: 
pb  —  pa  =  initial  pressure  ; 
/,  =  pg  —  back-pressure  ; 
PC  —  pbVb  ~  vc ; 


COMPOUND    ENGINES.  2/1 

Pt  =  PSVS  -T-  Vt\ 

Pd=Pn  =   \PcVc  +  P~(Vm  +  O!    H-   (Vc  +  Vm  +  Vr)  ' 
Pe=Po  =  Pd(Vc  +  Vm  +  Vr)  +  (Ve  +  V0  +  Vr)  ' 

Pf  =  P&e  +  t'r)  H-  (vf  +  vr)  ; 

A  =  Pk  =  {  Pf(vf  +  vr)  +  ptvt\  +  (Vf  +vt+  vr}  ; 

A  =  Pi  =  Ps(vf  +  vt  +.zv)  -i-Vi  +  Vt-}-  vr)  ; 

Pm  =  P&l  +  Vr)  4-  (Vm  +  Vr)  • 

Pi  —  phvh  -^  ^  ; 


The  pressures  /c  and  /w  can  be  found  directly  from  the 
initial  pressure  and  the  back-pressure,  and  finally  the  last  two 
equations  give  direct  calculations  for  p{  and  pp  so  soon  as  ph 
and  p0  are  found.  There  remain  six  equations  containing  six 
unknown  quantities,  which  can  be  readily  solved  after  numeri- 
cal values  are  assigned  to  the  known  pressures  and  to  all  the 
volumes. 

The  expansion  and  compression  lines,  be  and  hi,  for  the 
high-pressure  diagrams  are  hyperbolae  referred  to  the  axis  OV 
and  OP\  and  in  like  manner  the  expansion  and  compression 
lines  op  and  st,  for  the  low-pressure  diagram  are  hyperbolae 
referred  to  O'  V  and  O'P'  .  The  curve  ef  is  an  hyperbola 
referred  to  O'V  and  O  'P  ',  and  the  curve  Im  is  an  hyperbola 
referred  to  OV  and  OP.  The  transfer  lines  de  and  no,  gh 
and  >&/,  are  not  hyperbolae.  They  may  be  plotted  point  by 
point  by  finding  corresponding  intermediate  piston  positions, 
px  and  py,  by  aid  of  Fig.  64,  and  then  calculating  the  pressure 
for  these  positions  by  the  equation 


The  work  and  mean  effective  pressure  may  be  calculated 
in  a  manner  similar  to  that  given  for  the  direct-expansion 
engine  ;  but  the  calculation  is  tedious,  and  involves  two  trans- 
fers, de  and  no,  and  gh  and  kl.  The  first  involves  only  an 
expansion,  and  presents  no  special  difficulty;  the  second  con- 
sists of  a  compression  and  an  expansion,  which  can  be  dealt 


2/2  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

with  most  conveniently  by  a  graphical  construction.  All 
things  considered,  it  is  better  to  plot  the  diagrams  to  scale 
and  determine  the  areas  and  mean  effective  pressures  by  aid 
of  a  planimeter. 

If  the  cut-off  of  the  low-pressure  is  earlier  than  half-stroke 
so  as  to  precede  the  release  of  the  high-pressure  cylinder  the 
transfer  represented  by  de  and  no,  Fig.  63,  does  not  occur. 
Instead  there  is  a  compression  from  </to/and  an  expansion 
from  /  to  ///.  The  number  of  unknown  quantities  and  the 
number  of  equations  are  reduced.  On  the  other  hand  a 
release  before  the  end  of  the  stroke  of  the  high-pressure  piston 
requires  an  additional  unknown  quantity  and  one  more 
equation. 

Triple  Engines. — The  diagrams  from  triple  and  other 
multiple-expansion  engines  are  likely  to  show  much  irregu- 
larity, the  form  depending  on  the  number 
and  arrangement  of  the  cylinders  and  the 
sequence  of  the  cranks.  A  common  ar- 
rangement for  a  triple  engine  is  to  have 
three  pistons  acting  on  cranks  set  equidis- 
tant around  the  circle,  as  shown  by  Fig. 
65.  Two  cases  arise  depending  on  the 
sequence  of  the  cranks,  which  may  be  in  the 
order,  from  one  end  of  the  engine,  of  high-pressure,  low- 
pressure,  and  intermediate,  as  shown  by  Fig.  65  ;  or  in  the 
order  of  high-pressure,  intermediate,  and  low-pressure. 

With  the  cranks  in  the  order  high-pressure,  low-pressure, 
and  intermediate,  as  shown  by  Fig.  65,  the  diagrams  are  like 
those  given  by  Fig.  66.  The  admission  and  expansion  for 
the  high-pressure  cylinder  are  represented  by  abc.  When  the 
high- pressure  piston  is  at  release,  its  crank  is  at  //,  Fig.  65, 
and  the  intermediate  crank  is  at  /,  so  that  the  intermediate 
piston  is  near  half-stroke.  If  the  cut-off  for  that  cylinder  is 
later  than  half-stroke,  it  is  in  communication  with  the  first 
receiver  when  its  crank  is  at  /,  and  steam  may  pass  through 
the  first  receiver  from  the  high-pressure  to  the  intermediate 


COMPOUND    ENGINES. 


273 


cylinder,  and  there  is  a  drop  cd,  and  a  corresponding  rise  of 
pressure  no  in  the  intermediate  cylinder.  The  transfer  con- 
tinues till  cut-off  for  the  intermediate  cylinder  occurs  at  pr 
corresponding  to  the  piston  position  e  for  the  high-pressure 


Scale  160 


Atmospheric  line 


Atmospheric  line     i 


FIG.  66. 

cylinder.  From  the  position  e  the  high-pressure  piston  moves 
to  the  end  of  the  stroke  at  f,  causing  an  expansion,  and  then 
starts  to  return,  causing  the  compression  fg.  When  the 
high-pressure  piston  is  at  g  the  intermediate  cylinder  takes 
steam  at  the  other  end,  causing  the  drop  gh  and  the 
rise  of  pressure  xL  Then  follows  a  transfer  of  steam 
from  the  high-pressure  to  the  intermediate  cylinder  repre- 
sented by  hi  and  Im.  At  i  the  high-pressure  compression  ik 


274  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

begins,  and  is  carried  so  far  as  to  produce  a  loop  at  k.  After 
compression  for  the  high-pressure  cylinder  shuts  it  from  the 
first  receiver,  the  steam  in  that  receiver  and  in  the  inter- 
mediate cylinder  expand  as  shown  by  mn.  The  expansion  in 
the  intermediate  cylinder  is  represented  by  pq  and  the  release 
by  qr,  corresponding  to  a  rise  of  pressure  a/3  in  the  low- 
pressure  cylinder,  rs  and  j3y  represent  a  transfer  of  steam 
from  the  intermediate  cylinder  to  the  low-pressure  cylinder. 
The  remainder  of  the  back-pressure  line  of  the  intermediate 
cylinder  and  the  upper  part  of  the  low-pressure  diagram  for 
the  low-pressure  cylinder  correspond  to  the  same  parts  of  the 
high-pressure  and  the  intermediate  cylinders,  so  that  a  state- 
ment of  the  actions  in  detail  does  not  appear  necessary. 

The  equations  for  calculating  the  pressure  are  numerous, 
but  they  are  not  difficult  to  state,  and  the  solution  for  a  given 
example  presents  no  special  difficulty.  Thus  we  have 

pa  •=  pi,  =  initial  pressure; 

PC  =  pWb  •*-  Vc\ 

pd=  p0  =  \  pcvc  -f  pn(Vo  +  Vr)}   -*-  (vd 

Pe=pp  =  Pd(vd  +  V0  +  Vr)  ~5~  Ve  +  Vfi 

Pf  =  p^Ve  +  Vr)  •+•  (Vf  +  Vr); 

PS  =  Pf(Vf  +   Vr)  •+•  (Vg  +   Vr); 

ph  =  Pi  —   |  pg(Vg  +   Vr)  +  pxVx  }  -5-  (Vk  +  VI  -f  Vr)\ 

Pi  —  pm  =  ph(vh  +  VI  4-  Vr)   -*-  (V{  +  Vm  +  Vr)j 

/A  =  /«»»•  -^-  ^*; 

pn  —  p,n(Vm  +  Vr)  "*•  (Vn  +  »r); 


Pr  —  p$  = 
Ps—p-i—  pr(Vr  +  Va  +   V*)  H-  (»,  +  Wy  -f  Z//?)) 

//  =  ^s(z/s  -h  z/j?)  •*•  (^  +  VR)  ; 
^M  =  ^(^  -f-  VR)  -5-  (w»  +  z>*)  ; 

/„  =   )  pu(vu  -f-  »/?)  +  /rjfr,  }  -*-  (^  +  Vr,  +  VR)  \ 
pw—  PV(VT,  +  Vy  +  W^)   -5-  (Z/W  +  V*  +  VJ?)j 
/*  =  /»VW  -5-  Vx\ 

pa.  =  (%  +  VR)  -+•  (vo.  +  VR); 

P&  =  pava  -*-  VS; 

pe  =  pc,  =  back-pressure; 


COMPOUND   ENGINES.  2/5 

The  pressures  at  c  and  at  rj  can  be  calculated  immediately 
from  the  initial  pressure  and  from  the  back-pressure.  Then  it 
will  be  recognized  that  there  are  four  individual  equations  for 
finding /y,  /*,  pt,  and/5.  The  fourteen  remaining  equations, 
solved  as  simultaneous  equations,  give  the  corresponding 
fourteen  required  pressures,  some  of  which  are  used  in  calcu- 
lating the  four  pressures  which  are  determined  by  the  four 
individual  equations. 

If  the  cut-off  for  the  intermediate  cylinder  occurs  before 
the  release  of  the  high-pressure  cylinder,  then  the  transfer 
represented  by  de  and  op  does  not  occur.  In  like  manner,  if 
the  cut-off  for  the  low-pressure  cylinder  occurs  before  the 
release  for  the  intermediate  cylinder,  the  transfer  represented 
by  rs  and  fiy  does  not  occur.  The  omission  of  a  transfer  of 
course  simplifies  the  work  of  deducing  and  of  solving  equa- 
tions. 

In  much  the  same  way,  equations  may  be  deduced  for 
calculating  pressures  when  the  cranks  have  the  sequence 
high-pressure,  intermediate,  and  low-pressure.  The  dia- 
grams take  forms  which  are  distinctly  unlike  those  for  the 
other  sequence  of  cranks.  In  general,  the  case  solved, 
i.e.,  high-pressure,  low-pressure,  and  intermediate,  gives  a 
smoother  action  for  the  engine. 

for  example,  the  engines  of  the  U.  S.  S.  Machias  have 
the  following  dimensions  and  proportions: 

High-          Inter-          Low- 
pressure,     mediate,     pressure. 

Diameter  of  piston,  inches I5f  22^  35 

Piston  displacement,  cubic  feet 2.71         5.53  13.39 

Clearance,  per  cent 13  14  7 

Cut-off,  per  cent  stroke 66  66  66 

Release,       "            "        93  93  93 

Compression,  per  cent  stroke 18  18  18 

Ratio  of  piston  displacements I  2.04  4.94 

Volume  first  receiver,  cubic  feet 2.22 

Volume  second     "           "         "   6.26 

Ratio  of  receiver  volumes  to   high-pressure    piston 

displacement 0.82  2.31 

Stroke,  inches 24 

Boiler-pressure,  absolute,  pounds  per  sq.  in 180 

Pressure  in  condenser,             "         ••«««« 2 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


If  the  volume  of  the  high-pressure  piston  displacement  is 
taken  to  be  unity,  then  the  volumes  required  in  the  equations 


Scale  160 


FIG.  67. 

for  calculating  pressures,  when  the  cranks  have  the  order  high- 
pressure,  low-pressure,  and  intermediate,  are  as  follows: 

Vb   —  0.79  Vl   =  Vx  =  0.29  Vy  —  Vr,  =  0.35 

Ve  —  Vd  =   I  .O6    -        Vm  —  0.98  Vg  —  2.02 

ve  =  i.io  vn  =  v0  =  1.26  va  =  vp  —  2.72 

Vf  =   I.I3  ^  =    1.63  ZAy   =   3.60 

vs  —  vh  —  0.88         ^  =  z;r  =  2.18  2/5  =  z/«  =  4.94 

Vt  =  0.31  ^s  =  2.28  ^  =  1.23 

^  =  2^  =  0.13        ^  =  2.33 

vn  =  v.  =  1.85 

^w  =  0.63 


Pa=Pb=    150 

A  =  l65 

A-  112 

A  =  60-0 

A=A=7&5 

A  =  50.5 

A  =A  =  67-S 

pr=pt  = 

Pf  =  67.5 

P*=Py  = 

A  -  76-9 

Pi  -25.1 

PK=PI  =  73-5 

A  -  29-0 

COMPOUND   ENGINES.  2JJ 

The  required  pressures  are: 

pw  —  ps  =  25.6 
A  =  52.3 

A  =  22. 1 

3          A  =  18.5 
=  A  =  25-3        A=A  =  5 
A  =  17-6 

A  =  A  =  ^3       A  =  A  =  28.2 

Diagrams  with  the  volumes  and  pressures  corresponding 
to  this  example  are  plotted  in  Fig.  66  with  convenient 
vertical  scales.  Actual  indicator-diagrams  taken  from  the 
engine  are  given  by  Fig.  67.  The  events  of  the  stroke  come 
at  slightly  different  piston  positions  on  account  of  the  irregu- 
larity due  to  the  connecting-rod,  and  the  drops  and  other 
fluctuations  of  pressure  are  gradual  instead  of  sudden ;  more- 
over, there  is  considerable  loss  of  pressure  from  the  boiler  to 
the  engine,  from  one  cylinder  to  another,  and  from  the  low- 
pressure  cylinder  to  the  condenser.  Nevertheless  the  general 
forms  of  the  diagrams  are  easily  recognized  and  all  apparent 
erratic  variations  are  accounted  for. 

Designing  Compound  Engines. — The  designer  of  com- 
pound and  multiple-expansion  engines  should  have  at  hand 
a  well-systematized  fund  of  information  concerning  the  sizes, 
proportions,  and  powers  of  such  engines,  together  with  actual 
indicator-diagrams.  He  may  then,  by  a  more  or  less  direct 
method  of  interpolation  or  exterpolation,  assign  the  dimen- 
sions and  proportions  to  a  new  design,  and  can,  if  deemed 
advisable,  draw  or  determine  a  set  of  probable  indicator- 
diagrams  for  the  new  engines.  If  the  new  design  differs  much 
from  the  engines  for  which  he  has  information  he  may  deter- 
mine approximate  diagrams  both  for  an  actual  engine  from 
which  indicator-diagrams  are  at  hand,  and  for  the  new  design. 
He  may  then  sketch  diagrams  for  the  new  engine,  using  the 
approximate  diagrams  as  a  basis  and  taking  a  comparison  of 


278 


THERMODYNAMICS  OF   THE  STEAM-ENGINE. 


the  approximate  and  actual  diagrams  from  the  engine  already 
built,  as  a  guide.  It  is  convenient  to  prepare  and  use  a  table 
showing  the  ratios  of  actual  mean  effective  pressures  and 
approximate  mean  effective  \  ressures.  Such  a  table  enables 
the  designer  to  assign  mean  effective  pressures  to  a  cylinder 
of  the  new  engine  and  to  infer  very  closely  what  its  horse- 
power will  be.  It  is  also  very  useful  as  a  check  in  sketching 
probable  diagrams  for  a  new  engine,  which  diagrams  are 
not  only  useful  in  estimating  the  power  of  the  new  engine, 
but  in  calculating  stresses  on  the  members  of  that  engine. 

A  rough  approximation  of  the  power  of  an  engine  may  be 
made  by  calculating  the  power  as  though  the  total  or  equiva- 
lent expansion  took  place  in  the  low-pressure  cylinder,  neg- 
lecting clearance  and  compression.  The  power  thus  found  is 
to  be  affected  by  a  factor  which  according  to  the  size  and  type 
of  the  engine  may  vary  from  0.6  to  0.9  for  compound  engines 
and  from  0.5  to  O.8  for  triple  engines.  Seaton  and  Roun- 
thwaite  *  give  the  following  table  of  multipliers  for  compound 
marine  engines: 


MULTIPLIERS    FOR    FINDING    PROBABLE    M.E.P. 
AND  TRIPLE  MARINE   ENGINES. 


COMPOUND 


Description  of  Engine. 

Jacketed. 

Unjacketed. 

0.67  to  0.73 

0.58  to  0.68 

do                    paddle  engines.  .  .  . 

o  5^  to  o  65 

0.71  to  0.7^ 

Three  cylinder  triple,  merchant  ships  

0.64  to  0.68 

0.60  to  o.  66 

do                   naval  vessels            . 

o  KC  to  o  6^ 

do                   gunboats  and   torpedo 
boats 

o  60  to  o  67 

For  example,  let  the  boiler-pressure  be  80  pounds  by  the 
gauge,  or  94.7  pounds  absolute;  let  the  back-pressure  be 
4  pounds  absolute;  and  let  the  total  number  of  expansions  be 
six,  so  that  the  volume  of  steam  exhausted  to  the  condenser 
is  six  times  the  volume  admitted  from  the  boiler.  Neglect- 


*  Pocket  Book  of  Marine  Engineering. 


COMPOUND   ENGINES.  279 

ing  the  effect  of  clearance  and  compression,  the  mean  effective 
pressure  is 

94-7  X  |  +  94-7  X  i  log,  \  -  4  X  i  =  40.06  =  M.E.P. 

If  the  large  cylinder  is  30  inches  in  diameter,  and  the 
stroke  is  4  feet,  the  horse-power  at  60  revolutions  per  minute 
is 


—     X  40.06  X  2  X  4  X  60  -T-  33000  =  412  H.P. 

4 

If  the  factor  to  be  used  in  this  case  is  0.75,  then  the  actual 
horse-power  will  be  about 

0.75  X  400  =  300  H.P. 


CHAPTER  XIII. 
TESTING    STEAM-ENGINES. 

THE  principal  objects  of  tests  of  steam-engines  is  to  de- 
termine the  cost  of  power.  Series  of  engine  tests  are  made 
to  determine  the  effect  of  certain  conditions,  such  as  super- 
heating and  steam-jackets,  on  the  economy  of  the  engine. 
Again,  tests  may  be  made  to  investigate  the  interchanges  of 
heat  between  the  steam  and  the  walls  of  the  cylinder  by  the 
.aid  of  Hirn's  analysis,  and  thus  find  how  certain  conditions 
produce  effects  that  are  favorable  or  unfavorable  to  economy. 

The  two  main  elements  of  an  engine  test  are,  then,  the 
measurement  of  the  power  developed  and  the  determination 
of  the  cost  of  the  power  in  terms  of  thermal  units,  pounds  of 
steam,  or  pounds  of  coal.  Power  is  most  commonly  measured 
by  aid  of  the  steam-engine  indicator,  but  the  power  delivered 
by  the  engine  is  sometimes  determined  by  a  dynamometer  or  a 
friction  break;  sometimes,  when  an  indicator  cannot  be  used 
conveniently,  the  dynamic  or  break  power  only  is  deter- 
mined. When  the  engine  drives  a  dynamo-electric  generator 
the  power  applied  to  the  generator  may  be  determined  elec- 
trically, and  thus  the  power  delivered  by  the  engine  may  be 
known. 

When  the  cost  of  power  is  given  in  terms  of  coal  per 
liorse-power  per  hour,  it  is  sufficient  to  weigh  the  coal  for  a 
-definite  period  of  time.  In  such  case  a  combined  boiler  and 
engine  test  is  made,  and  all  the  methods  and  precautions  for  a 
careful  boiler  test  must  be  observed.  The  time  required  for 
such  a  test  depends  on  the  depth  of  the  fire  on  the  grate  and 

280 


TESTING   STEAM-ENGINES.  28 1 

the    rate  of  combustion.      For  factory  boilers  the  test  should 
be  twenty-four  hours  long  if  exact  results  are  desired. 

When  the  cost  of  power  is  stated  in  terms  of  steam  per 
horse-power  per  hour,  one  of  two  methods  may  be  followed. 
When  the  engine  has  a  surface  condenser  the  steam  exhausted 
from  the  engine  is  condensed,  collected,  and  weighed.  One 
hour  is  usually  sufficient  for  tests  under  favorable  conditions ; 
shorter  intervals,  ten  or  fifteen  minutes,  give  fairly  uniform 
results.  The  chief  objection  to  this  method  is  that  the  ar 
pumped  from  the  condenser  is  saturated  with  moisture  which  is 
not  accounted  for.  The  error  from  this  source  is  probably  not 
important,  for  the  results  of  tests  by  this  method  and  by  de- 
termining the  feed-water  supplied  to  the  boiler  are  substan- 
tially the  same.  In  tests  on  non-condensing  and  on  jet-con- 
densing engines  the  steam  consumption  is  determined  by 
weighing  or  measuring  the  feed-water  supplied  to  the  boiler 
or  boilers  that  furnish  steam  to  the  engine.  Steam  used  for 
any  other  purpose  than  running  the  engine,  for  example,  for 
pumping,  heating,  or  making  determinations  of  the  quality  of 
the  steam,  must  be  determined  and  allowed  for.  -The  most 
satisfactory  way  is  to  condense  and  weigh  such  steam,  but 
small  quantities,  as  for  determining  quality  by  a  steam  calo- 
rimeter, may  be  gauged  by  allowing  it  to  flow  through  an 
orifice.  Tests  which  depend  on  measuring  the  feed-water 
should  be  long  enough  to  minimize  the  effect  of  the  uncer- 
tainty of  the  amount  of  water  in  a  boiler  corresponding  to  an 
apparent  height  of  water  in  a  water-gauge ;  for  the  apparent 
height  of  the  water-level  depends  largely  on  the  rate  of  vapor- 
ization and  the  activity  of  convection  currents. 

When  the  cost  of  power  is  expressed  in  thermal  units  it  is 
necessary  to  measure  the  steam  pressure,  the  amount  of  moisture 
in  the  steam  supplied  to  the  cylinder,  and  the  temperature  of 
the  condensed  steam  when  it  leaves  the  condenser.  If  steam 
is  used  in  jackets  or  reheaters  it  must  be  accounted  for  sepa- 
rately. But  it  is  customary  in  all  engine  tests  to  take  pressures 
and  temperatures,  so  that  the  cost  may  usually  be  calculated  in 


282  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

thermal  units,  even  when  the  experimenter  is  content  to  state 
it  in  pounds  of  steam. 

For  a  Hirn's  analysis  it  is  necessary  to  weigh  or  measure 
the  condensing  water,  and  to  determine  the  temperatures  at 
admission  to  and  exit  from  the  condenser. 

Important  engines,  with  their  boilers  and  other  appurte- 
nances, are  commonly  built  under  contract  to  give  a  certain 
economy,  and  the  fulfilment  of  the  terms  of  a  contract  is  de- 
termined by  a  test  of  the  engine  or  of  the  whole  plant.  The 
test  of  the  entire  plant  has  the  advantage  that  it  gives,  as  one 
result,  the  cost  of  power  directly  in  coal ;  but  as  the  engine  is 
often  watched  with  more  care  during  a  test  than  in  regular 
service,  and  as  auxiliary  duties,  such  as  heating  and  banking 
fires,  are  frequently  omitted  from  such  an  economy  test,  the 
actual  cost  of  power  can  be  more  justly  obtained  from  a  rec- 
ord of  the  engine  in  regular  service,  extending  for  weeks  or 
months.  The  tests  of  engine  and  boilers,  though  made  at  the 
same  time,  need  not  start  and  stop  at  the  same  time,  though 
there  is  a  satisfaction  in  making  them  strictly  simultaneous. 
This  requires  that  the  tests  shall  be  long  enough  to  avoid 
drawing  the  fires  at  beginning  and  end  of  the  boiler  test. 

In  anticipation  of  a  test  on  an  engine  it  must  be  run  for 
some  time  under  the  conditions  of  the  test,  to  eliminate 
the  effects  of  starting  or  of  changes.  Thus  engines  with 
steam-jackets  are  commonly  started  with  steam  in  the  jackets, 
even  if  they  are  to  run  with  steam  excluded  from  the  jackets. 
An  hour  or  more  must  then  be  allowed  before  the  effect 
of  using  steam  in  the  jackets  will  entirely  pass  away.  An 
engine  without  steam-jackets,  or  with  steam  in  the  jackets, 
may  come  to  constant  conditions  in  a  fraction  of  that  time,  but 
it  is  usually  well  to  allow  at  least  an  hour  before  starting 
the  test. 

It  is  of  the  first  importance  that  all  the  conditions  of  a  test 
shall  remain  constant  throughout  the  tests.  Changes  of  steam- 
pressure  are  particularly  bad,  for  when  the  steam-pressure 
rises  the  temperature  of  the  engine  and  all  parts  affected 


TESTING   STEAM-ENGINES.  283 

by  the  steam  must  be  increased,  and  the  heat  required  for  this 
purpose  is  charged  against  the  performance  of  the  engine  ;  if 
the  steam-pressure  falls  a  contrary  effect  will  be  felt.  In  a  series 
of  tests  one  element  at  a  time  should  be  changed,  so  that  the 
effect  of  that  element  may  not  be  confused  by  other  changes, 
even  though  such  changes  have  a  relatively  small  effect.  It 
is,  however,  of  more  importance  that  steam-pressure  should 
remain  constant  than  that  all  tests  at  a  given  pressure  should 
have  identically  the  same  steam-pressure,  because  the  total 
heat  of  steam  varies  more  slowly  than  the  temperature. 

All  the  instruments  and  apparatus  used  for  an  engine  test 
should  be  tested  and  standardized  either  just  before  or  just 
after  the  test  ;  preferably  before,  to  avoid  annoyance  when 
any  instrument  fails  during  the  test  and  is  replaced  by  another. 

Thermometers. — Temperatures  are  commonly  measured 
by  aid  of  mercurial  thermometers,  of  which  three  grades  may 
be  distinguished.  For  work  resembling  that  done  by  the 
physicist  the  highest  grade  should  be  used,  and  these  must 
ordinarily  be  calibrated,  and  have  their  boiling-  and  freezing- 
points  determined  by  the  experimenter  or  some  qualified 
person ;  since  the  freezing-point  is  liable  to  change,  it  should 
be  redetermined  when  necessary.  For  important  data  good 
thermometers  must  be  used,  such  as  are  sold  by  reliable 
dealers,  but  it  is  preferable  that  they  should  be  calibrated  or 
else  compared  with  a  thermometer  that  is  known  to  be  reliable. 
For  secondary  data  or  for  those  requiring  little  accuracy 
common  thermometers  with  the  graduation  on  the  stem  may 
be  used,  but  these  also  should  have  their  errors  determined 
and  allowed  for.  Thermometers  with  detachable  scales  should 
be  used  only  for  crude  work. 

Gauges. — Pressures  are  commonly  measured  by  Bourdon 
gauges,  and  if  recently  compared  with  a  correct  mercury 
column  these  are  sufficient  for  engineering  work.  The  columns 
used  by  gauge-makers  are  commonly  subject  to  minor  errors, 
and  are  not  usually  corrected  for  temperature.  It  is  important 
that  such  gauges  should  be  frequently  retested.  From  their 


284  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

convenience  vacuum-gauges  of  the  same  form  are  used,   even 
where  a  mercurial  gauge  could  easily  be  applied. 

The  pressure  of  the  atmosphere  may  be  taken  with  either  a 
mercurial  or  an  aneroid  barometer,  but  if  the  latter  is  used  its 
errors  must  be  known.  It  should  be  easy  to  make  the  baro- 
metric errors  only  a  fraction  of  the  unavoidable  gauge  errors. 

Dynamometers. — The  standard  for  measurement  of  power 
is  the  friction-brake.  For  smooth  continuous  running  it  is 
essential  that  the  brake  and  its  band  shall  be  cooled  by  a  stream 
of  water  that  does  not  come  in  contact  with  the  rubbing  surfaces. 
Sometimes  the  wheel  is  cooled  by  a  stream  of  water  circulating 
through  it,  sometimes  the  band  is  so  cooled,  or  both  may  be. 
A  rubbing  surface  which  is  not  cooled  should  be  of  non-con- 
ducting material.  If  both  rubbing  surfaces  are  metallic  they 
must  be  freely  lubricated  with  oil.  An  iron  wheel  running  in 
a  band  furnished  with  blocks  of  wood  requires  little  or  no 
lubrication. 

To  avoid  the  increase  of  friction  on  the  brake-bearings  due 
to  the  load  applied  at  a  single  brake-arm  two  equal  arms  may 
be  used  with  two  equal  and  opposite  forces  applied  at  the  ends 
to  form  a  statical  couple. 

With  care  and  good  workmanship  a  friction-brake  may  be 
made  an  instrument  of  precision  sufficient  for  physical  investi- 
gations, but  with  ordinary  care  and  workmanship  it  will  give 
results  of  sufficient  accuracy  for  engineering  work. 

All  forms  of  transmission  dynamometers  should  be  stand- 
ardized, and  should  have  their  errors  determined  by  compari- 
son with  a  friction-brake. 

Indicators. — The  most  important  and  at  the  same  time  the 
least  satisfactory  instrument  used  in  engine-testing  is  the 
indicator.  Even  when  well  made  and  in  good  condition  it  is 
liable  to  have  an  error  of  two  per  cent  or  more  when  used  at 
moderate  speeds.  At  high  speeds,  three  hundred  revolutions 
per  minute  and  over,  it  is  likely  to  have  two  or  three  times  as 
much  error.  As  a  rule,  an  indicator  cannot  be  used  at  more 
than  four  hundred  revolutions  per  minute. 


TESTING    STEAM-EXGIXES.  285 

The  mechanism  for  reducing  the  motion  of  the  crosshead 
of  the  engine  and  transferring  it  to  the  paper  drum  of  an 
indicator  should  be  correct  in  design  and  free  from  undue 
looseness.  It  should  require  only  a  very  short  cord  leading  to 
the  paper  drum,  because  all  the  errors  due  to  the  paper  drum 
are  proportional  to  the  length  of  the  cord  and  may  be  prac- 
tically eliminated  by  making  the  cord  short. 

The  weighing  and  recording  of  the  steam-pressure  by  the 
indicator-piston,  pencil-motion,  and  pencil  are  affected  by 
errors  which  may  be  classified  as  follows  : 

1.  Scale  of  the  spring. 

2.  Design  of  the  pencil-motion. 

3.  Inertia  of  moving  parts. 

4.  Friction  and  backlash. 

Good  indicator-springs,  when  tested  by  direct  loads  out  of 
the  indicator,  usually  have  correct  and  uniform  scales  ;  that  is, 
they  collapse  under  pressure  the  proper  amount  for  each  load 
applied.  The  springs  are  perceptibly  weaker  at  high  tempera- 
tures than  at  ordinary  temperatures,  but  when  used  on  a  steam- 
engine  they  are  exposed  to  steam  but  little,  if  any,  above  the 
pressure  of  the  atmosphere,  and  are  but  little  affected  thereby. 
Some  recent  indicators  have  the  spring  above  the  cylinder,  so 
that  it  is  not  exposed  to  steam.  If  the  scale  of  a  spring 
is  uniform,  but  is  either  more  or  less  than  the  rated  scale,  a 
correction  can  easily  be  applied.  Thus  a  spring  marked  for 
50  pounds  to  the  inch  may  be  really  a  48-pound  spring,  if  the 
indicator-pencil  rises  an  inch  for  48-pounds  increase  of  pres- 
sure. But  a  spring  having  an  irregular  scale  must  be  rejected, 
as  there  is  no  convenient  way  of  applying  corrections  for 
irregular  errors,  especially  when  the  area  of  the  diagram 
is  measured  by  a  planimeter. 

The  motion  of  the  piston  of  the  indicator  is  multiplied  five 
or  six  times  by  the  pencil-motion,  which  is  usually  an  approx- 
imate parallel  motion.  Within  the  proper  range  of  motion 
(about  two  inches)  the  pencil  draws  a  line  which  is  nearly 


286  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

straight  when  the  paper  drum  is  at  rest,  and  it  gives  a  nearly 
uniform  scale  provided  that  the  spring  is  uniform.  The  errors 
due  to  the  geometric  design  of  this  part  of  the  indicator  are 
always  small. 

When  steam  is  suddenly  let  into  the  indicator,  as  at  ad- 
mission to  the  engine-cylinder,  the  indicator-piston  and  at- 
tached parts  forming  the  pencil-motion  are  set  into  vibration, 
with  a  natural  time  of  vibration  depending  on  the  stiffness  of 
the  spring.  A  weak  spring  used  for  indicating  a  high-speed 
engine  may  throw  the  diagram  into  confusion,  because  the 
pencil  will  give  a  few  deep  undulations  which  make  it  impos- 
sible to  recognize  the  events  of  the  stroke  of  the  engine,  such 
as  cut-off  and  release.  A  stiffer  spring  will  give  more  rapid 
and  less  extensive  undulations,  which  will  be  much  less  trouble- 
some. As  a  rule,  when  the  undulations  do  not  confuse  the 
diagram  the  area  of  the  diagram  is  but  little  affected  by  the 
undulations  due  to  the  inertia  of  the  piston  and  pencil-motion. 

The  largest  and  most  troublesome  errors  of  the  indicator 
are  due  to  friction  and  backlash.  The  various  joints  at  the 
piston  and  in  the  pencil-motion  are  made  as  tight  as  can  be 
without  undue  friction,  but  there  is  always  some  looseness  and 
some  friction  at  those  joints.  There  is  also  some  friction  of 
the  piston  in  the  cylinder  and  of  the  pencil  on  the  paper. 
Errors  from  this  source  are  commonly  one  or  two  per  cent, 
and  may  be  excessive  unless  the  instrument  is  used  with  care 
and  skill.  A  blunt  pencil  pressed  up  hard  on  the  paper  will 
reduce  the  area  of  the  diagram  five  per  cent  or  more ;  on  the 
other  hand  a  medium  pencil  drawing  a  faint  but  legible  line 
will  affect  the  area  very  little.  Any  considerable  friction  of 
the  piston  of  the  indicator  will  destroy  the  value  of  the  diagram. 

Errors  of  the  scale  of  the  spring  can  be  readily  determined 
and  investigated  by  loading  the  spring  with  known  weights, 
when  properly  supported,  out  of  the  indicator.  Other  tests  of 
the  indicator  are  difficult  and  are  likely  to  be  misleading,  as  in 
general  such  tests  consist  in  comparing  the  indicator  with  either 
a  mercury  column  or  a  gauge  when  subjected  to  the  same 


TESTING   STEAM-ENGINES. 

pressure.  Now  a  gauge,  and  stilPmore  a  mercury  column,  can 
be  used  only  for  measuring  steady  prSlure,  while  an  indicator- 
piston  is  sure  to  show  excessive  friction  if  it  does  not  stick 
fast  when  exposed  to  a  steady  pressure.  The  consequence  is 
that  a  test  made  by  changing  pressure  progressively  on  both 
an  indicator  and  a  gauge  or  mercury  column  is  likely  to  lead  to 
errors  in  the  indications  of  both  instruments.  The  only  satis- 
factory way  of  testing  an  indicator  is  to  subject  it  to  changing 
pressure,  so  as  to  simulate  the  action  of  steam  in  the  cylinder 
of  an  engine,  and  to  measure  the  pressure  with  a  mercury  col- 
umn or  a  gauge.  The  two  pressures  may  differ  by  five  or  ten 
pounds  and  may  be  varied  progressively  at  a  rate  adapted  to 
the  use  of  a  mercury  column  or  gauge.  Very  few  instruments 
for  thus  testing  indicators  have  been  made,  and  they  have  not 
yet  been  adapted  to  commercial  work.  Such  investigations 
show  that  the  error  of  an  indicator  need  not  be  more  than  one 
or  two  per  cent. 

Scales. — Weighing  should  be  done  on  scales  adapted  to 
the  load;  overloading  leads  to  excessive  friction  at  the  knife- 
edges  and  to  lack  of  delicacy.  Good  commercial  platform 
scales,  when  tested  with  standard  weights,  are  sufficient  for 
engineering  work. 

Coal  and  ashes  are  readily  weighed  in  barrows,  for  which 
the  tare  is  determined  by  weighing  empty.  Water  is  weighed 
in  barrels  or  tanks.  The  water  can  usually  be  pumped  in  or 
allowed  to  run  in  under  a  head,  so  that  the  barrel  or  tank  can 
be  filled  promptly.  Large  quick-opening  valves  must  be  used 
to  allow  the  water  to  run  out  quickly.  As  the  receptacle  will 
seldom  drain  properly,  it  is  not  well  to  wait  for  it  to  drain,  but 
to  close  the  exit-valve  and  weigh  empty  with  whatever  small 
amount  of  water  may  be  caught  in  it.  Neither  is  it  well  to  try 
to  fill  the  receptacle  to  a  given  weight,  as  the  jet  of  water 
running  in  may  affect  the  weighing.  With  large  enough  scales 
and  tanks  the  largest  amounts  of  water  used  for  engine  tests 
may  be  readily  handled. 

Measuring  Water. — When  it  is  not  convenient  to  weigh 


288  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

water  directly  it  may  be  measured  in  tanks  or  other  receptacles 
of  known  volume.  Commonly  two  are  used,  so  that  one  may 
fill  while  the  other  is  emptied.  The  volume  of  a  receptacle 
may  be  calculated  from  its  dimensions  or  may  be  determined 
by  weighing  in  water  enough  to  fill  it.  When  desired  a 
receptacle  may  be  provided  with  a  scale  showing  the  depth  of 
the  water,  and  so  partial  volumes  can  be  determined.  A  closed 
receptacle  may  be  used  to  measure  hot  water  or  ether  fluids. 
Water  metres  are  of  two  kinds:  some  measure  the 
water  by  the  displacement  of  a  piston  or  of  pistons ;  in  others  the 
water  is  recorded  by  a  rotating  piece  which  is  commonly  made 
of  a  material  having  nearly  the  density  of  water.  The  latter 
may  serve  to  check  the  use  of  water  drawn  from  a  city  water- 
supply,  but  they  are  seldom  reliable  enough  for  use  in  engine- 
testing.  Piston  water-metres  can  be  made  to  give  almost  any 
desired  degree  of  accuracy ;  good  commercial  piston-metres 
seldom  have  more  than  one  or  two  per  cent  of  error.  They 
should  always  be  tested  under  the  conditions  of  the  test, 
taking  account  of  both  the  amount  and  the  temperature  of 
the  water  measured.  Tests  of  marine  engines  can  hardly  be 
made  without  the  aid  of  a  metre.  For  such  tests  the  metre 
may  be  placed  on  a  by-pass  through  which  the  feed-water 
from  the  surface- condenser  can  be  made  to  pass  by  closing  a 
valve  on  the  direct  line  of  feed-pipe.  If  necessary  the  metre 
can  be  quickly  shut  off  and  the  direct  line  can  be  opened. 
The  chief  uncertainty  in  the  use  of  a  metre  is  due  to  air  in 
the  water ;  to  avoid  error  from  this  source  the  metre  should 
be  frequently  vented  to  allow  air  to  escape  without  being 
recorded  by  the  metre. 

Weirs  and  Orifices. — So  far  as  possible  the  use  of  weirs 
and  orifices  for  water  during  engine  tests  should  be  avoided, 
for,  in  addition  to  the  uncertainties  unavoidably  connected 
with  such  hydraulic  measurements,  difficulties  are  liable  to 
arise  from  the  temperature  of  the  water  and  from  the  oil  in  it. 
A  very  little  oil  is  enough  to  sensibly  affect  the  coefficient  for 
a  weir  or  orifice.  The  water  flowing  from  the  hot-well  of  a 


TESTING   STEAM-ENGINES.  289 

jet-condensing  engine  is  so  large  in  amount  that  it  is  deemed 
advisable  to  measure  it  on  a  weir ;  the  effect  of  temperature 
and  oil  is  less  than  when  the  same  method  is  used  for 
measuring  condensed  steam  from  a  surface-condenser. 

Calorimeters. — When  superheated  steam  is  supplied  to 
an  engine  it  is  sufficient  to  take  the  temperature  of  the  steam 
in  the  steam-pipe  near  the  engine.  When  moist  steam  is 
used  the  condition  of  the  steam  must  be  determined  by 
a  calorimetric  experiment.  Four  kinds  of  calorimeters  will 
be  described  out  of  a  large  number  that  have  been  used 
by  different  experimenters  and  at  different  times.  They  are 
the  barrel  calorimeter,  the  Barrus  continuous  water-calorim- 
eter, the  throttling-calorimeter,  and  the  separating  calorim- 
eter. 

The  Barrel  Calorimeter. — A  wooden  barrel  set  on  scales 
is  provided  with  a  large  valve  for  emptying  it,  and  provision 
is  made  for  filling  it  with  cold  water,  usually  from  a  hydrant- 
pipe,  and  for  bringing  the  steam  to  be  tested.  Some  form 
of  stirrer  must  be  used,  a  good  form  being  a  wooden  propeller- 
wheel  on  a  wooden  shaft  with  a  hand-crank. 

The  method  of  making  a  test  is  as  follows :  The  barrel  is 
weighed  empty,  and  a  suitable  quantity  of  cold  water  is  run  in 
and  weighed.  The  temperature  of  the  cold  water  should  be 
taken  as  it  enters.  The  steam-pipe  usually  terminates  in  a 
piece  of  rubber  hose  which  may  be  swung  into  or  out  of  the 
barrel.  When  the  barrel  is  nearly  filled  with  cold  water  the 
steam-valve  may  be  opened  until  all  condensed  water  is  blown 
from  the  pipe  and  the  hose  is  warmed  up ;  then  the  hose  may 
be  swung  into  the  barrel  and  steam  may  be  run  into  the  water 
till  a  proper  amount  is  condensed.  A  preliminary  calculation 
will  determine  the  proper  weights  of  water  and  steam  to  give 
a  good  range  of  temperatures  in  the  calorimeter.  After  the 
steam  is  run  in  the  water  in  the  barrel  may  be  well  stirred 
and  the  highest  temperature  taken  as  the  final  temperature. 

To  eliminate  the  action  of  the  wood  of  the  barrel  one  or 
more  tests  are  made  and  rejected,  and  the  times  of  running  irk 


2QO  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

water  and  steam  are  made  equal,  so  that  the  barrel,  which  is 
already  warmed  by  the  preceding  test,  may  give  up  as  much 
heat  during  one  part  of  the  process  as  it  receives  during  the 
other  part. 

If  the  pressure  of  the  steam  is/,  and  the  part  of  each  pound 
-of  the  mixture  which  is  steam  is  represented  by  x,  while  the 
initial  and  final  temperatures  of  the  water  are  tl  and  £,  ,  and 
.the  weights  of  the  water  and  steam  are  W  and  w,  then 

w(xr  +  ?  —  ?,)  =  W(q^  -  q,)  ; 

-?.)  (26) 


wr 

r  and  q  being  the  latent  heat  and  heat  of  the  liquid  for  the 
pressure  p,  and  ql  and  q^  being  the  heats  of  the  liquid  for  the 
temperatures  /,  and  t^  . 

For  example,  suppose  that  180  pounds  of  water  at  the  tem- 
perature of  60°.  2  F.  are  run  into  a  barrel  calorimeter,  and  that 
the  final  temperature  of  the  water  in  the  calorimeter  is  103°.  6 
F.,  after  7^  pounds  of  steam  at  73.8  pounds  by  the  gauge  are 
run  in  and  condensed.  At  an  absolute  pressure  of  88.5 
pounds  r  =  890.4,  q  —  288.8;  the  heats  of  the  liquid  at 
60°,  2  and  103°.  6  are  28.32  and  71.6. 

=  180(71.6-28.32)-  7.25(288.8-71.6) 
7.25  X  890.4 

consequently  the  per  cent  of  priming  is  3.7. 

It  is  to  be  remarked  of  this  kind  of  calorimeter  that  satis- 
factory results  are  difficult  to  attain  even  when  every  care  and 
precaution  are  used,  and  that  a  small  error  in  determining  the 
weight  of  steam,  which  is  obtained  by  subtraction,  makes  a 
large  difference  in  the  result. 

Continuous  Water-calorimeter.  —  The  difficulty  of  ob- 
taining the  weight  of  steam  with  sufficient  accuracy  which 
occurs  in  the  use  of  the  barrel  calorimeter  is  avoided  in  the  use 
of  the  continuous  water-calorimeter,  represented  by  Fig.  68. 
This  calorimeter  is  essentially  a  small  surface-condenser  ~{ 


TESTING   STEAM-ENGINES. 


29I 


special  form,  so  arranged  that  the  condensed  steam  is  weighed 
separately  from  the  cooling  water. 

Steam  is  brought  to  the  calorimeter  by  the  pipey,  with  the 
gauge  i  for  giving  the  pressure.     The  pipe  a,  which  forms  the 


COLD  WATER 


FIG.  68. 

condensing  surface,  and  which  may  conveniently  be  made  of 
brass  pipe  one  inch  in  diameter,  should  have  the  joints,  above 
and  below,  clear  of  the  bucket  containing  the  cooling  water. 
Steam  is  let  into  the  pipe  a  at  full  boiler-pressure,  and  the  con- 
densed water  gathers  in  the  pipe  below,  where  the  water-level 
is  shown  at  e.  The  height  of  the  water  at  e  is  kept  constant 
by  aid  of  the  valve  at  d,  which  may  have  a  long  wooden  handle 


2Q2  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

attached  for  convenient  regulation.  At  h  there  is  a  thermome- 
ter to  determine  the  temperature  of  the  condensed  steam. 
Since  this  temperature  is  only  a  little  less  than  that  due  to  the 
boiler-pressure,  the  condensed  water  should  be  led  through  a 
cooler  like  a  simple  surface-condenser,  with  a  separate  stream 
of  cooling  water,  and  the  cooled  water  may  be  collected  and 
weighed  on  suitable  scales. 

The  cooling  water  for  the  calorimeter  is  brought  by  the 
pipe  b  with  a  valve  for  regulating  the  supply,  and  is  led  away 
to  a  barrel  on  scales  by  the  pipe  c,  with  a  valve  to  regulate  the 
height  of  the  water  in  the  bucket.  To  insure  a  good  circula- 
tion and  a  proper  mingling  of  the  cooling  water  the  current  is 
directed  through  a  rubber  hose  to  the  bottom  of  the  inner 
cylinder  around  the  pipe  a,  thence  up  and  into  the  top  of 
the  outer  cylinder,  thence  down  and  out  at  the  bottom  of  this 
cylinder  and  over  a  weir  at  the  exit.  The  temperatures  of  the 
cooling  water  at  entrance  and  exit  are  taken  by  the  thermom- 
eters f  and  g,  which  should  be  reliable  to  -fa  of  one  degree 
Fahrenheit. 

The  pipe  j  leading  to  the  calorimeter  and  the  pipe  con- 
taining the  condensed  steam  should  be  well  wrapped  as  far  as 
to  the  valve  at  d.  At  k  there  is  a  brass  cone  to  protect  the 
covering  of  the  pipe  from  water. 

Though  not  essential,  it  is  convenient  to  line  the  bucket 
with  sheet  metal. 

In  preparing  for  a  test  the  water  and  steam  are  let  on 
and  properly  regulated,  and  the  calorimeter  is  allowed  to 
run  till  all  parts  may  be  assumed  to  be  at  a  constant  tem- 
perature ;  the  cooling  water  from  c  and  the  condensed  steam 
are  then  directed  into  the  receptacles  for  weighing,  and  the 
time  is  noted  as  the  beginning  of  the  test.  The  steam-pres- 
sure and  the  several  temperatures  are  taken  at  intervals  and 
recorded.  At  the  end  of  half  an  hour  or  an  hour  the 
cooling  water  and  condensed  water  are  diverted  from  the 
weighing  receptacles,  and  the  time  is  noted  as  the  end  of  the 
test.  The  quantities  of  the  cooling  and  condensed  water  can 


TESTING   STEAM-ENGINES.  293 

be  weighed  at  the  end  of  the  test,  or  the  test  may  be  made 
continuous  for  any  desired  length  of  time  by  having  two 
weighing  receptacles  for  each,  and  filling  and  emptying  them 
alternately. 

The  radiation  in  thermal  units  per  hour  must  be  deter- 
mined by  running  the  calorimeter  without  cooling  water  and 
with  the  bucket  filled  with  hair-felt. 

In  this  or  any  form  of  calorimeter  that  is  capable  of  giving 
accurate  results  it  is  essential  that  the  steam-pressure  should 
not  change  during  a  test,  since  a  considerable  change  of  pres- 
sure will  vitiate  the  results  on  account  of  the  heat  absorbed 
or  yielded  by  the  pipes  leading  to  the  condenser. 

Let  Wand  w  be  the  weights  of  the  cooling  water  for  the 
test,  and  let  p  be  the  steam-pressure  and  /3  the  final  tempera- 
ture of  the  condensed  steam  taken  by  the  thermometer  at  h, 
while  tl  and  /,  are  the  initial  and  final  temperatures  of  the  cool- 
ing water;  finally,  let  the  radiation  during  the  test  be  e  ther- 
mal units. 

Then 

w(xr  +  q  -  q^  =  W(q^  -q^  +  e; 

...  x  =  *?fo-y.)  +  *-tt<g-g.)a  (266) 

wr 

Example.  —  The  following  are  the  data  of  a  test  made  in 
the  laboratory  of  the  Institute  of  Technology  : 

Initial  temperature  of  cooling  water,     .  37°.  49  F. 

Final  "  "        "  "         .  83°.  84  F. 

Temperature  of  condensed  steam,    .      .  304°.  88  F. 
Pressure  of  the  atmosphere,    ....        14.8  Ibs.  per  sq.  in. 

Pressure  of  steam  by  gauge,  .      .      .      .        72.4    "      "     "     " 

Duration  of  test,      .......        40  minutes. 

Radiation  per  hour,       ......  180  B.  T.  u. 

Weight  of  cooling  water,  .....  573-5  pounds. 

condensed  water,   ....       29.89     " 

L9I   -   5-53)+  120  -  29.89(287.6  -  274.4)  . 

29.89  X  891.2 
x  =  0.988. 
Per  cent  of  priming,  1.2. 


'* 


294 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


It  is  apparent  that  any  surface-condenser  may  be  used  in 
the  same  manner  as  a  calorimeter,  except  that  it  is  not 
usually  convenient  to  fill  such  a  condenser  with  steam  at 
boiler-pressure.  Since  the  wire-drawing  of  steam  in  a  well- 
wrapped  valve  is  accompanied  with  little  loss  of  heat,  this 
need  not  interfere  with  such  a  use  of  a  condenser.  In 
an  engine  test  the  quality  of  exhaust-steam  flowing  to  a 
jet  or  a  surface  condenser  can  be  determined  by  equation 
(265)  or  (266),  except  that  the  external  radiation  cannot 
always  be  satisfactorily  determined. 

Throttling-calorimeter — A  simple  form  of  calorimeter, 
devised  by  the  author,  is  shown  by  Fig.  69,  where  A  is  a 
reservoir  about  four  inches  in  diameter 
and  about  10  inches  long  to  which 
steam  is  admitted  through  a  half-inch 
pipe  b,  with  a  throttle  valve  near  the 
reservoir.  Steam  flows  away  through 
an  inch  pipe  d.  At./"  is  a  gauge  for 
measuring  the  pressure,  and  at  e  there 
is  a  deep  cup  for  a  thermometer  to 
measure  the  temperature.  The  boiler- 
pressure  may  be  taken  from  a  gauge 
on  the  main  steam-pipe  near  the 
calorimeter.  It  should  not  be  taken 
from  a  pipe  in  which  there  is  a  rapid 
flow  of  steam  as  in  the  pipe  b,  since 
the  velocity  of  the  steam  will  affect  the 
gauge-reading,  making  it  less  than  the 
real  pressure.  The  reservoir  is  wrapped 

with  hair-felt  and   lagged  with  wood  to  reduce  radiation  'of 
heat. 

When  a  test  is  to  be  made,  the  valve  on  the  pipe  d  is 
opened  wide  (this  valve  is  frequently  omitted)  and  the  valve 
at  b  is  opened  wide  enough  to  give  a  pressure  of  five  to  fifteen 
pounds  in  the  reservoir.  Readings  are  then  taken  of  the 
boiler-gauge,  of  the  gauge  at  /,  and  of  the  thermometer  at  e. 


TESTING   STEAM-ENGINES.  295 

It  is  well  to  wait  about  ten  minutes  after  the  instrument  is 
started  before  taking  readings  so  that  it  may  be  well  heated. 
Let  the  boiler-pressure  be  /,  and  let  r  and  q  be  the  latent 
heat  and  heat  of  the  liquid  corresponding.  Let  /,  be  the 
pressure  in  the  calorimeter,  and  hi  and  tl  the  total  heat  and 
the  temperature  of  saturated  steam  at  that  pressure,  while  /, 
is  the  temperature  of  the  superheated  steam  in  the  calorim- 
eter. Then 


.  .  .  .  (267) 


Example.  —  The    following   are    the  data  of  a  test  made 
with  this  calorimeter: 

Pressure  of  the  atmosphere  .........      14.8  pounds; 

Steam-pressure  by  gauge  ...........      69.8        " 

Pressure  in  the  calorimeter,  gauge...      12.0        " 
Temperature  in  the  calorimeter  .....    268°.  2  F. 

x  =  "SM  +  0.48(268.2  -  243.9)  -  285-3  =  Q    88  . 

892.7 
Per  cent  of  priming,   1.2. 

A  little  consideration  shows  that  this  type  of  calorimeter 
can  be  used  only  when  the  priming  is  not  excessive  ;  otherwise 
the  throttling  will  fail  to  superheat  the  steam,  and  in  such 
case  nothing  can  be  told  about  the  condition  of  the  steam 
either  before  or  after  throttling.  To  find  this  limit  for  any 
pressure  ts  may  be  made  equal  to  tl  in  equation  (267);  that  is, 
we  may  assume  that  the  steam  is  just  dry  and  saturated  at  that 
limit  in  the  calorimeter.  Ordinarily  the  lowest  convenient 
pressure  in  the  calorimeter  is  the  pressure  of  the  atmosphere,  or 
14.7  pounds  to  the  square  inch.  The  table  following  has  been 
calculated  for  several  pressures  in  the  manner  indicated.  It 
shows  that  the  limit  is  higher  for  higher  pressures,  but  that 
the  calorimeter  can  be  applied  only  where  the  priming  is 
moderate. 

When  this  calorimeter  is  used  to  test  steam  supplied  to  a 
condensing-engine  the  limit  may  be  extended  by  connecting 


296 


THERMODYNAMICS   OF    THE   STEAM-ENGINE. 


the  exhaust  to  the  condenser.  For  example,  the  limit  at  100 
pounds  absolute,  with  3  pounds  absolute  in  the  calorimeter,  is 
0.064,  instead  of  0.046  with  atmospheric  pressure  in  the  calo- 
rimeter. 

LIMITS   OF  THE   THROTTLING   CALORIMETER. 


PRESSURE. 

Priming. 

Absolute. 

Gauge. 

300 

285.3 

0.077 

250 

235-3 

0.070 

200 

185.3 

0.061 

175 

160.3 

0.058 

ISO 

135-3 

0.052 

125 

H0.3 

0.046 

100 

85-3 

0.040 

75 

60.3 

0.032 

50 

35.3 

0.023 

In  case  the  calorimeter  is  used  near  its  limit — that  is,  when 
the  superheating  is  a  few  degrees  only — it  is  essential  that  the 
thermometer  should  be  entirely  reliable ;  otherwise  it  might 
happen  that  the  thermometer  should  show  superheating  when 
the  steam  in  the  calorimeter  was  saturated  or  moist.  In  any 
other  case  a  considerable  error  in  the  temperature  will  produce 
an  inconsiderable  effect  on  the  result.  Thus  at  100  pounds 
absolute  with  atmospheric  pressure  in  the  calorimeter  10°  F. 
of  superheating  indicates  0.035  priming,  and  15°  F.  indicates 
0.032  priming.  So  also  a  slight  error  in  the  gauge-reading  has 
little  effect.  Suppose  the  reading  to  be  apparently  100.5 
pounds  absolute  instead  of  100,  then  with  10°  of  superheat- 
ing the  priming  appears  to  be  0.033  instead  of  0.032. 

It  has  been  found  by  experiment  that  no  allowance  need 
be  made  for  radiation  from  this  calorimeter  if  made  as  described, 
provided  that  200  pounds  of  steam  are  run  through  it  per 
hour.  Now  this  quantity  will  flow  through  an  orifice  one- 
fourth  of  an  inch  in  diameter  under  the  pressure  of  70  pounds 
by  the  gauge,  so  that  if  the  throttle-valve  be  replaced  by  such 
an  orifice  the  question  of  radiation  need  not  be  considered. 
In  such  case  a  stop-valve  will  be  placed  on  the  pipe  to  shut 


TES  TING   S  TEA  M-ENGINES. 


297 


off  the  calorimeter  when  not  in  use ;  it  is  opened  wide  when  a 
test  is  made.  If  an  orifice  is  not  provided  the  throttle-valve 
may  be  opened  at  first  a  small  amount,  and  the  temperature 
in  the  calorimeter  noted ;  after  a  few  minutes  the  valve  may  be 
opened  a  trifle  more,  whereupon  the  temperature  may  rise,  if 
too  little  steam  was  used  at  first.  If  the  valve  is  opened  little 
by  little  till  the  temperature  stops  rising  it  will  then  be  certain 
that  enough  steam  is  used  to  reduce  the  error  from  radiation 
to  a  very  small  amount. 

Various  modifications  of  the  throttling-calorimeter  have 
been  proposed,  mainly  with  a  view  to  reducing  its  size  and 
weight.  Almost  any  of  them  will  prove  satisfactory  in  prac- 
tice, but  some  will  be  found  to  be  liable  to  error  from  radia- 
tion or  from  the  fact  that  there  is  not  sufficient  opportunity 
for  the  steam  to  come  to  rest  and  properly  develop  the  super- 
heating due  to  throttling. 

Separating  Calorimeter. — If  steam  contains  more  than 
three  per  cent  of  moisture  the  priming 
may  be  determined  by  a  good  sepa- 
rator which  will  remove  nearly  all  the 
moisture.  It  remains  to  measure  the 
steam  and  water  separately.  The  water 
may  be  best  measured  in  a  calibrated 
vessel  or  receiver,  while  the  steam  may 
be  condensed  and  weighed,  or  may  be 
gauged  by  allowing  it  to  flow  through 
an  orifice  of  known  size.  A  form  of 
separating  calorimeter  devised  by  Prof. 
Carpenter*  is  shown  by  Fig.  70. 

Steam  enters  a  space  at  the  top 
which  has  sides  of  wire  gauze  and  a 
convex  cup  at  the  bottom.  The  water 
is  thrown  against  the  cup  and  finds  its 
way  through  the  gauze  into  an  inside 
chamber  or  receiver  and  rises  in  a  FlG-  TO. 


*  Trans.  Am.  Soc.  Meek.  Engs.,  vol.  xvii,  p.  608. 


298  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

water-glass  outside.  The  receiver  is  calibrated  by  trial,  so 
that  the  amount  of  water  may  be  read  directly  from  a  gradu- 
ated scale.  The  steam  meanwhile  passes  into  the  outer  cham- 
ber which  surrounds  the  inner  receiver  and  escapes  from  an 
orifice  at  the  bottom.  The  steam  may  be  determined  by  con- 
densing, collecting,  and  weighing  it ;  or  it  may  be  calculated 
from  the  pressure  and  the  size  of  the  orifice.  When  the  steam 
is  weighed  there  is  no  radiation  error,  since  the  inner  cham- 
ber is  protected  by  the  steam  in  the  outer  chamber.  This 
instrument  may  be  guarded  against  radiation  by  wrapping 
and  lagging,  and  then  if  steam  enough  is  used  the  radiation 
will  be  insignificant,  just  as  was  found  to  be  the  case  for  the 
throttling-calorimeter. 

There  is  a  question  whether  this  instrument  or  the  throt- 
tling-calorimeter should  be  called  a  calorimeter;  perhaps  they 
may  be  better  considered  to  be  priming-gauges. 

Method  of  Sampling  Steam — It  is  customary  to  take  a 
sample  of  steam  for  a  calorimeter  or  priming-gauge  through  a 
small  pipe  leading  from  the  main  steam-pipe.  The  best 
method  of  securing  a  sample  is  an  open  question;  indeed,  it 
is  a  question  whether  we  ever  get  a  fair  sample.  There  is  no 
question  but  that  the  composition  of  the  sample  is  correctly 
shown  by  any  of  the  calorimeters  described,  when  the 
observer  makes  tests  with  proper  care  and  skill.  It  is 
probable  that  the  best  way  is  to  take  steam  through  a 
pipe  which  reaches  at  least  halfway  across  the  main  steam- 
pipe,  and  which  is  closed  at  the  end  and  drilled  full  of 
small  holes.  It  is  better  to  have  the  sampling-pipe  at  the  side 
or  top  of  the  main,  or  otherwise  arranged  so  that  water  tric- 
kling along  the  bottom  of  the  main  shall  not  enter  the  calo- 
rimeter. Again,  it  is  better  to  take  a  sample  from  a  pipe 
through  which  steam  flows  vertically  upward.  The  sampling- 
pipe  should  be  short  and  well  wrapped  to  avoid  radiation. 

Indirect  Engine  Test — It  is  often  difficult,  if  not  impos- 
sible, to  determine  the  steam  used  by  an  engine  directly  if  it 
has  not  a  surface-condenser,  and  if  at  the  same  time  the  boiler 


TESTING   STEAM-ENGINES.  299 

or  boilers  supplying  it  with  steam  do  other  work  also.  If  the 
engine  has  a  jet-condenser  then  the  overflow  from  the  hot-well 
may  be  determined  by  allowing  it  to  flow  over  a  weir.  At  the 
same  time  the  engine  may  be  indicated  and  the  temperatures 
of  the  cold  injection-water  and  of  the  overflow  from  the  hot- 
well  may  be  determined.  If  possible  the  priming  in  the 
steam-pipe  should  be  determined  by  aid  of  a  throttling  calo- 
rimeter, and  if  the  engine  has  a  steam-jacket  the  radiation  may 
be  found  from  the  condensation  of  steam  in  the  jackets  while 
the  engine  is  at  rest.  For  approximate  work  the  steam  in  the 
supply-pipe  may  be  assumed  to  be  dry,  and  the  radiation  may 
be  inferred  from  comparison  with  an  engine  of  the  same  size 
and  type  ;  or,  since  the  radiation  is  nearly  constant,  it  may  be 
treated  as  a  constant  unknown  error. 

Suppose  that  the  engine  uses  M  pounds  of  steam  per  horse- 
power per  hour,  and  that  G  pounds  of  condensing  water  are 
used  per  pound  of  exhaust-steam  ;  then 


(268) 


is  equal  to  the  overflow  of  the  hot-well  in  pounds  per  hour  as 
determined  by  the  aid  of  a  weir. 

If  the  injection-water  comes  in  at  the  temperature  /,  and 
flows  from  the  hot-well  with  the  condensed  steam  at  the 
temperature  tk,  then  the  heat  taken  up  by  the  condensing 
water  is 

MG(qk  —  ?,), 

where  qk  and  q{  are  the  heats  of  the  liquid  corresponding  to  the 
temperatures  tk  and  /,-.  The  heat  radiated  per  hour  may  be 
represented  by  R.  The  heat  changed  into  work  will  be 

60  H.P. 


33000 

where  H.P.  represents  the  horse-power  of  the  engine   deter- 
mined from  the  indicator-diagrams. 


30O  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

The  heat  supplied  to  the  engine  per  hour  will  be 
M(xr  +  q-  qk), 

where  r  and  q  are  the  heat  of  vaporization  and  heat  of  the 
liquid  at  the  pressure/  in  the  steam-pipe,  and  x  is  the  quality 
of  the  steam;  usually,  x  is  between  0.98  and  unity.  This 
equation  assumes  that  the  feed-water  is  drawn  from  the  hot- 
well  at  the  temperature  tk. 

But  the  heat  supplied  to  the  engine  is  equal  to  the  heat 
accounted  for  as  work,  by  radiation,  and  as  carried  away  by 
the  cooling  water,  so  that  we  have 


60  H  P 
M(xr  +  q  -  ft)  =  2  -  +  R  +  MG(  q,  -  ?,).'   (269) 

jjUUU 

a  _  :jt*.w 

From  equations  (268)  and  (269)  we  have 
60  H.P. 


nooo 

33000  _     ^ 


^  +  q  -  & 

by  which  the  steam  per  horse-power  can  be  readily  calculated, 
and  the  thermal  units  per  horse-power  per  minute  can  be  found 
from  the  expression 

+  g-gk)+6o.     .     .     .     .    (271) 


CHAPTER    XIV. 
INFLUENCE    OF    THE    CYLINDER    WALLS. 

THE  difference  between  the  action  of  steam  in  the  cylinder 
of  a  steam-engine  and  the  calculated  action  of  steam  in  a  non- 
conducting cylinder  is  due  mainly  to  the  influence  of  the 
walls  of  the  cylinder,  on  which  steam  condenses  during  admis- 
sion and  from  which  water  is  vaporized  during  expansion  and 
exhaust.  This  influence  is  so  intense,  and  at  the  same  time 
so  complicated,  that  any  attempt  to  base  the  design  of  a  steam- 
engine  on  the  theoretical  discussion  of  the  cycle  for  a  non-con- 
ducting engine  leads  only  to  confusion  and  disappointment. 
This  became  evident  as  soon  as  an  attempt  was  made  to  use 
the  results  of  the  thermodynamic  investigations  of  Rankine 
and  Clausius  for  that  purpose,  and  in  consequence  the  whole 
thermodynamic  treatment  of  the  properties  of  steam  and  of  its 
application  to  the  production  of  power  was  looked  upon  with 
disfavor  by  engine-builders.  Tests  on  engines  showed  an 
actual  steam-consumption  of  quarter  or  half  more  than  was 
given  by  theoretical  calculations;  and,  again,  the  conditions 
which  the  theory  indicated  as  favorable  to  economy  often 
gave  the  worst  results.  This  discrepancy  between  theory  and 
practice  was  most  notable  in  the  case  of  cut-off  and  expansion 
in  the  cylinder.  Thus  on  page  238  it  is  shown  that 
complete  expansion  to  the  back-pressure  gives  a  higher  effi- 
ciency than  incomplete  expansion  with  a  drop  at  release.  But 
many  experiments,  for  example  those  by  Isherwood  on  the 
U.  S.  S.  Michigan  in  1861,  showed  conclusively  that  the  best 
economy  was  obtained  by  use  of  a  moderately  short  cut-off. 

301 


302 


THERMODYNAMICS  OF   THE   STEAM-ENGINE, 


From  the  accompanying  table  of  conditions  and  results  it 
appears  that  for  the  engines  of  the  Michigan  the  best  econ- 
omy in  steam-consumption  is  given  for  a  cut-off  at  %  of 
the  stroke.  The  same  result  is  shown  even  more  clearly  by  a 
diagram  in  which  each  cut-off  is  laid  off  as  an  abscissa  and  the 
corresponding  steam-consumption  is  laid  off  as  an  ordinate,  as 

shown  by  Fig.  71. 
To  make  the  dia- 
gram clear  and  com- 
pact, the  axis  of  ab- 
scissae is  taken  at  30 
pounds  of  steam  per 
horse- power  per 
hour.  An  inspection 
of  this  diagram  and 
of  the  figures  in  the 
table  show  a  regu- 
larity in  the  results 


U.S. s.  MICHIGAN 

Abscissae  per  cents  of  cut  off 
Ordinates  pounds  of  steam 
per  horse  power  per  hour. 


0.2 


0.4 

FIG. 


0.6 


which  can  be  at- 
tained only  when 
tests  are  made  with  care  and  skill.  The  only  condition  pur- 
posely varied  is  the  cut-off;  the  only  condition  showing  im- 
portant accidental  variation  is  the  vacuum,  and  consequently 
the  back-pressure  in  the  cylinder.  To  allow  for  the  small 
variations  in  the  back-pressure  Isherwood  changed  the  mean 
effective  pressure  for  each  test  by  adding  or  subtracting,  as 
the  case  might  require,  the  difference  between  the  actual 
back-presure  and  the  mean  back-pressure  of  2.7  pounds  per 
square  inch,  as  deduced  from  all  the  tests. 

An  inspection  of  any  such  a  series  of  tests  having  a  wide 
range  of  expansions  will  show  that  the  steam-consumption 
decreases  as  the  cut-off  is  shortened  till  a  minimum  is  reached, 
usually  at  J  to  £  stroke ;  any  further  shortening  of  the  cut-off 
will  be  accompanied  by  an  increased  steam-consumption, 
which  may  become  excessive  if  the  cut-off  is  made  very  short. 
Some  insight  into  the  reason  for  this  may  be  had  from  the 


INFLUENCE   OF   THE    CYLINDER    WALLS.  303 

TABLE    II. 

TESTS  ON  THE  ENGINE  OF  THE  U.  S.  S.  MICHIGAN. 

CYLINDER    DIAMETER,  36   INCHES  ;    STROKE,   8    FEET. 

By  Chief-Engineer   ISHERWOOD,  Researches  in  Experimental  Steam 


Engineering. 

I. 

II. 

72 

7/10 
15-6 

19  5 
29.8 
26.  i 
33-8 
15-3 

III. 

72 
4/9 
17-3 

21.0 

29-7 
26.3 

32.7 
27-2 

IV. 

72 

3/io 
13-7 

21.0 
30.1 

25-8 

34-7 
41.7 

V. 

72 
1/4 
13-9 

21.  0 
29-9 

25-8 
34-5 
39-6 

VI. 

72 
1/6 

II.  2 

21  .O 

29.9 
25.6 
36.8 
42.1 

VII. 

72 

4/45 
14.1 

22.0 
29.9 
24-1 
41-4 

45-i 

Duration    hours  

72 

11/12 
20.6 

21.0 
3O.I 
26.5 
38.0 
10.7 

Cut-off                               .... 

Boiler-pressure,  pounds  per  sq.  in.  above 

Barometer   inches  of  mercury        .        .  . 

Vacuum    inches  of  mercury  

Steam  per  horse-power  perhour,  pounds 
Percent  of  water  in  cylinder  at  release. 

per  cent  of  water  in  the  cylinder,  calculated  from  the  dimen- 
sions of  the  cylinder  and  the  pressures  in  the  cylinder  taken 
from  the  indicator-diagram.  The  method  of  the  calculation 
will  be  given  in  detail  a  little  later  in  connection  with  Hirn's 
analysis.  It  will  be  sufficient  now  to  notice  that  the  amount 
of  water  in  the  cylinder  of  the  engine  of  the  Michigan  at 
release  increased  from  10.7  per  cent  for  a  cut-off  at  -J-J  of  the 
stroke  to  45.1  per  cent  for  a  cut-off  at  ^  of  the  stroke. 
Now  all  the  water  in  the  cylinder  at  release  is  vapor- 
ized during  the  exhaust,  the  heat  for  this  purpose  being 
abstracted  from  the  cylinder  walls,  and  the  heat  thus 
abstracted  is  wasted,  without  any  compensation.  The  walls 
may  be  warmed  to  some  extent  in  consequence  of  the  rise  of 
pressure  and  temperature  during  compression,  but  by  far  the 
greater  part  of  the  heat  abstracted  during  exhaust  must  be 
supplied  by  the  incoming  steam  at  admission.  There  is 
therefore  a  large  condensation  of  steam  during  admission  and 
up  to  cut-off,  and  the  greater  part  of  the  steam  thus  con- 
densed remains  in  the  form  of  water  and  does  little  if  any- 
thing toward  producing  work.  This  may  be  seen  by  inspec- 
tion of  the  table  of  results  of  Dixwell's  tests  on  page  371. 
With  saturated  steam  and  with  cut-off  at  0.217  of  the 

*  ^J 

stroke,  52.2  per  cent  of  the  working  substance  %the  cylinder 


304  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

was  water.  Of  this  19.8  per  cent  was  reevaporated  during 
expansion  and  32.4  per  cent  remained  at  release  to  be  re- 
evaporated  during  exhaust.  When  the  cut-off  was  lengthened 
to  0.689  °f  tne  stroke,  there  was  27.9  per  cent  of  water  at 
cut-off  and  23.9  per  cent  at  release.  The  statement  in  per- 
centages gives  a  correct  idea  of  the  preponderating  influence 
of  the  cylinder  walls  when  the  cut-off  is  unduly  shortened ;  it 
is,  however,  not  true  that  there  is  more  condensation  with  a 
short  than  with  a  long  cut-off.  On  the  contrary  there  is  more 
water  condensed  in  the  cylinder  when  the  cut-off  is  long,  only 
the  condensation  does  not  increase  as  fast  as  do  the  weight  of 
steam  supplied  to  the  cylinder  and  the  work  done,  and  conse- 
quently the  condensation  has  a  less  effect. 

Hirn's  Analysis — Though  the  method  just  illustrated 
gives  a  correct  idea  of  the  influence  of  the  walls  of  the 
cylinder  of  a  steam-engine,  our  first .  clear  insight  into  the 
action  of  the  walls  is  due  to  Him,*  who  accompanied  his 
exposition  by  quantitative  results  from  certain  engine  tests. 
The  statement  of  his  method  which  will  be  given  here  is  de- 
rived from  a  memoir  by  Dwelshauvers-Dery.f 

Let  Fig.  72  represent  the  cylinder  of  a  steam-engine  and 
the  diagram  of  the  actual  cycle.  For  sake  of  simplicity  the 
diagram  is  represented  without  lead  of 
admission  or  release,  but  the  equations  to 
be  deduced  apply  to  engines  having  either 
or  both.  The  points  I,  2,  3,  and  o  are 
the  points  of  cut-off,  release,  compression, 
and  admission.  The  part  of  the  cycle 
from  o  to  I,  that  is,  from  admission  to 


FlG  cut-off,  is  represented  by  a ;    in  like  man- 

ner, b,  c,    and   d  represent   the   parts   of 

the  cycle  during  expansion,  exhaust,  and   compression.      The 
numbers  will  be  used  as  subscripts  to  designate  the  properties 

*  Bulletin  de  la  Soc.  Ind.   de  Mulhotise,  1873  \    The'orie  Mtchanique  de  la 
Chaleur,  vol.  ii.,  1876. 

f  Revue  universelle  des  Mines,  vol.  viii.  p.  362,  1880. 


INFLUENCE   OF   THE   CYLINDER    WALLS.  3°  5 

of  the  working  fluid  under  the  conditions  represented  by  the 
points  indicated,  and  the  letters  will  be  used  in  connection 
with  the  operations  taking  place  during  the  several  parts  of 
the  cycle.  Thus  at  cut-off  the  pressure  is  /t,  and  the  tem- 
perature, heat  of  the  liquid,  heat  of  vaporization,  condition, 
etc.,  are  represented  by  tlt  q^  rlt  x^  etc.  The  external  work 
from  cut-off  to  release  is  Wb,  and  the  heat  yielded  by  the 
walls  of  the  cylinder  due  to  reevaporation  is  Qb. 

Suppose  that  M  pounds  of  steam  are  admitted  to  the 
cylinder  per  stroke,  having  in  the  supply-pipe  the  pressure  p 
and  the  condition  x\  that  is.  each  pound  is  x  part  steam 
mingled  with  i  —  x  of  water.  The  heat  brought  into  the 
cylinder  per  stroke,  reckoned  from  freezing-point,  is 

Q  =  M(q  +  xr) (272) 

Should  the  steam  be  superheated  in  the  supply-pipe  to 
the  temperature  /„  then 

Q  =  M\\  +  cp(t.  -  /)],  ....  (273) 
in  which  cp  =  0.4805  is  the  specific  heat  of  superheated  steam 
at  constant  pressure. 

Let  the  heat-equivalent  of  the  intrinsic  energy  of  the  entire 
weight  of  water  and  steam  in  the  cylinder  at  any  point  of  the 
cycle  be  represented  by  /  ;  then  at  admission,  cut-off,  release, 
and  compression  we  have 

/.  =  M.(q0  +  x0p.)  ; (274> 

7,  =  (M  +  M.)(q,  +  xlPl) ;       .   '  .      .  (275) 

7,  =  (M+M^  +  ^,);  ....  (276) 

73  =  M,(q,  +  *3ps) ; (277) 

in  which  p  is  the  heat-equivalent  of  the  internal  work  due  to 
vaporization  of  one  pound  of  steam,  and  M0  is  the  weight  of 
water  and  steam  caught  in  the  cylinder  at  compression,  cal- 
culated in  a  manner  to  be  described  hereafter. 

If  the  steam  is  superheated  at  any  point  of  the  cycle 
the  corresponding  intrinsic  energy  may  be  calculated  by  aid  of 


306          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

equation  (179),  page  133.    For  example  the  heat-equivalent  of 
the  intrinsic  energy  at  release  may  be 

/,  =  (M  4-  M.)  \  j4-  A<».  -  *,)  +  ft  +  /»,  [  .  (278) 


where  v^  is  the  specific  volume  of  the  superheated  steam  and 
j,  is  the  specific  volume  of  saturated  steam  at  the  pressure/,. 

k  is,  of  course,  the  constant  --,  as  given  on  page  129. 

At  admission  the  heat-equivalent  of  the  fluid  in  the 
cylinder  is  70,  and  the  heat  supplied  by  the  entering  steam  up 
to  the  point  of  cut-off  is  Q.  Of  the  sum  of  these  quantities  a 
part,  A  Wa,  is  used  in  doing  external  work,  and  a  part  remains 
as  intrinsic  energy  at  cut-off.  The  remainder  must  have  been 
absorbed  by  the  walls  of  the  cylinder,  and  will  be  represented 
by  Qa.  Hence 

0.=  Q  +  I.-I.-AW.. 

From  cut-off  to  release  the  external  work  W*  is  done,  and 
at  release  the  heat-equivalent  of  the  intrinsic  energy  is  /,. 
Usually  the  walls  of  the  cylinder,  during  expansion,  supply 
heat  to  the  steam  and  water  in  the  cylinder.  To  be  more 
explicit,  some  of  the  water  condensed  on  the  cylinder  walls 
during  admission  and  up  to  cut-off  is  evaporated  during  expan- 
sion. This  action  is  so  energetic  that  72  is  commonly  larger 
than  7j.  Since  heat  absorbed  by  the  walls  is  given  a  positive 
sign,  the  contrary  sign  should  be  given  to  heat  yielded  by 
them ;  it  is,  however,  convenient  to  give  a  positive  sign  to 
all  the  interchanges  of  heat  in  the  equations,  and  then  in 
numerical  problems  a  negative  sign  will  indicate  that  heat  is 
yielded  during  the  operation  under  consideration.  For  expan- 
sion, then, 

Qt  =  /,-/,-  A  Wb. 

During  the  exhaust  the  external  work  Wc  is  done  by  the 
engine  on  the  steam,  the  water  resulting  from  the  condensation 


INFLUENCE   OF   THE   CYLINDER    WALLS. 


307 


of  the  steam  in  the  condenser  carries  away  the  heat  Mq^  the 
cooling  water  carries  away  the  heat  G(qk  —  qt),  and  there 
remains  at  compression  the  heat-equivalent  of  intrinsic  energy 
/,.  So  that 

Qc  =  /,  -  7,  -  Mq<  -  G(qk  -  q.)  +  A  Wc, 

in  which  qt  is  the  heat  of  the  liquid  of  the  condensed  steam, 
and  G  is  the  weight  of  cooling  water  per  stroke  which  has  on 
entering  the  heat  of  the  liquid  q{,  and  on  leaving  the  heat  of 
the  liquid  qk. 

During  compression  the  external  work  Wd  is  done  by  the 
engine  on  the  fluid  in  the  cylinder,  and  at  the  end  of  com- 
pression, i.e.,  at  admission,  the  heat-equivalent  of  the  intrinsic 
energy  is  7o.  Hence 

Q*  =  /.-/.  +  A  Wd. 

It  should  be  noted  (Fig  72)  that  the  work  Wa  is  repre- 
sented by  the  area  which  is  bounded  by  the  steam  line,  the 
ordinates  through  o  and  I  and  by  the  axis  OV.  And  in  like 
manner  the  works  Wb,  Wc,  and  Wd  are  represented  by  areas 
which  extend  to  the  axis  OV.  In  working  up  the  analysis  from 
a  test  the  line  of  absolute  zero  of  pressure  may  be  drawn 
und^r  the  atmospheric  line  as  in  Fig. 
73,  or  proper  allowance  may  be  made 
after  the  calculation  has  been  made 
with  reference  to  the  atmospheric 
line. 

For  convenience  these  four  equa- 
tions will  be  assembled  as  follows : 


Atmospheric  line 


FIG.  73. 


Q*= 


(279) 
(280) 
(281) 
(282) 


308  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

A  consideration  of  these  equations  shows  that  all  the 
quantities  of  the  right-hand  members  can  be  obtained  directly 
from  the  proper  observations  of  an  engine  test  except  the 
several  values  of  /,  the  heat-equivalents,  of  the  intrinsic  ener- 
gies in  the  cylinder.  These  quantities  are  represented  by 
equations  (274)  to  (277),  in  which  there  are  five  unknown 
quantities,  namely  XQJ  xiy  x»  x^  and  Mo.  Should  the  steam 
be  superheated  at  any  point,  as  at  release,  the  proper  modifi- 
cation must  be  made  as  indicated  by  equation  (278),  in 
which  case  we  have  the  unknown  v%  instead  of  x^ 

Let  the  volume  of  the  clearance-space  between  the  valve 
and  the  piston  when  it  is  at  the  end  of  its  stroke  be  F0  ;  and 
let  the  volumes  developed  by  the  piston  up  to  cut-off  and 
release  be  Vl  and  Fa  ;  finally,  let  F3  represent  the  correspond- 
ing volume  at  compression.  The  specific  volume  of  one  pound 
of  mixed  water  and  steam  is 

V  =  XU  -\-  (T, 

and  the  volume  of  M  pounds  is 


At  the  points  of  admission,  cut-off,  release,  and  compres- 
sion 


u0+(r);.    ..      ..    .      .  (283) 

F0  +  Vt  =  (M  +  M^u,  +  er);      .      .  (284) 

r.+  r,=(M+M.)(*.ut  +  <r);      .     .  (285) 

r.+  r.  =  M.(*.ut+<r)  .....  (286) 

There  is  sufficient  evidence  that  the  steam  in  the  cylinder 
at  compression  is  nearly  if  not  quite  dry,  and  as  there  is  com- 
paratively little  steam  present  at  that  time,  there  cannot  be 
much  error  in  assuming 


INFLUENCE   OF   THE   CYLINDER    WALLS.  309 

This  assumption  gives,  by  equation  (286^, 


in  which  y3  is  the  density  or  weight  of  one  cubic  foot  of  dry 
steam  at  compression. 

Applying  this  result  to  equations  (283)  to  (286)  gives 

*.  =  T£T-?: (2g8) 


~     .....     (2QO) 


We  are  now  in  condition  to  find  the  values  of  70,  /,,  /„  and 
/„  and  consequently  can  calculate  all  the  interchanges  of  heat 
by  equations  (279)  to  (282). 

If  the  steam  is  superheated  at  some  point,  as  at  release, 
proper  allowance  must  of  course  be  made.  Thus  we  may 
have 


or 

V  A-  V 


which  gives  the  means  of  calculating  /,  by  equation  (278). 
The  fact  that  steam  is  superheated  will  be  indicated  by  an 
apparent  value  of  x  greater  than  unity  when  calculated  by  one 
of  the  equations  (288),  (289),  or  (290).  It  is  probable  that 
any  test  of  an  engine  with  much  compression  will  give  super- 
heated steam  at  admission  when  x0  is  calculated  by  equation 
(288).  Recent  tests  by  Callandar  and  Nicolson  confirm  the 
conclusions  from  such  calculations.  There  will,  however,  be 
little  error  in  most  cases  from  assuming  x^  to  be  unity  as  well 


310          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

as  x^,  and  the  work  will  be  a  little  simplified  by  such  an  assump- 
tion. It  may  be  remarked  in  passing  that  when  the  specific 
volume  and  pressure  of  superheated  steam  are  known  the 
temperature  may  be  calculated  by  equation  (i77)»  page  130. 
There  is,  however,  no  reason  except  general  interest  for 
making  such  a  calculation. 

In  the  diagram,  Fig.  72,  the  external  work  during  exhaust 
is  all  work  done  by  the  piston  on  the  fluid,  since  the  release  is 
assumed  to  be  at  the  end  of  the  stroke.  If  the  release  occurs 
before  the  end  of  the  stroke,  some  of  the  work,  namely,  from 
release  to  the  end  of  the  stroke,  will  be  done  by  the  steam 
on  the  piston,  and  the  remainder,  from  the  end  of  the  stroke 
back  to  compression,  will  be  done  by  the  piston  on  the  fluid. 
In  such  case  We  will  be  the  difference  between  the  second  and 
the  first  quantities.  If  an  engine  has  lead  of  admission,  a 
similar  method  may  be  employed ;  but  at  that  part  of  the 
diagram  the  curves  of  compression  and  admission  can  be  dis- 
tinguished with  difficulty,  if  at  all,  and  little  error  can  arise 
from  neglecting  the  lead. 

The  several  pressures  at  admission,  cut-off,  release,  and 
compression  are  determined  by  the  aid  of  the  indicator-dia- 
gram, and  the  pressures  in  the  steam-pipe  and  exhaust-pipe  or 
condenser  are  determined  by  gauges.  The  weight  M  of  steam 
supplied  to  the  cylinder  per  stroke  is  best  determined  by  con- 
densing the  exhaust-steam  in  a  surface-condenser  and  collect- 
ing and  weighing  it  in  a  tank.  If  the  engine  is  non-condens- 
ing, or  if  it  has  a  jet-condenser,  or  if  for  any  reason  this 
method  cannot  be  used,  then  the  feed-water  delivered  to  the 
boiler  may  be  determined  instead.  The  cooling  or  condensing 
water,  either  on  the  way  to  the  condenser  or  when  flowing 
from  it,  may  be  weighed,  or  for  engines  of  large  size  may  be 
measured  by  a  metre  or  gauged  by  causing  it  .to  flow  over  a 
weir  or  through  an  orifice.  The  several  temperatures  /4,  tiy 
and  tk  must  be  taken  by  proper  thermometers.  When  a  jet- 
condenser  is  used,  and  the  condensing  water  mingles  with  the 
steam,  /4  is  identical  with  tk.  The  quality  x  of  the  steam  in 


INFLUENCE   OF   THE    CYLINDER    WALLS.  311 

the  supply-pipe  must  be  determined  by  a  steam-calorimeter. 
A  boiler  with  sufficient  steam-space  will  usually  deliver  nearly 
dry  steam  ;  that  is,  x  will  be  nearly  unity.  If  the  steam  is 
superheated,  its  temperature  /,  may  be  taken  by  a  ther- 
mometer. 

Let  the  heat  lost  by  radiation,  conduction,  etc.,  be  Qe; 
this  is  commonly  called  the  radiation.  Let  the  heat  supplied 
by  the  jacket  be  Qj.  Of  the  heat  supplied  to  the  cylinder  per 
stroke,  a  portion  is  changed  into  work,  a  part  is  carried  away 
by  the  condensed  steam  and  the  cooling  or  condensing  water, 
and  the  remainder  is  lost  by  radiation  ;  therefore 


G,=  Q  +  Q~Mq-G(qk-q^-A(  Wa  +  Wt-  Wc-  Wd).    (292) 

The  heat  Qj  supplied  by  a  steam-jacket  may  be  calculated 
by  the  equation 

Q.=  m(x>r'  +  q'-q")  .....      (293) 

in  which  m  is  the  weight  of  water  collected  per  stroke  from  the 
jacket  ;  x1  ',  r',  and  q'  are  the  quality,  the  heat  of  vaporization, 
and  the  heat  of  the  liquid  of  the  steam  supplied;  and  q"  is  the 
heat  of  the  liquid  when  the  water  is  withdrawn.  When  the 
jacket  is  supplied  from  the  main  steam-pipe,  x'  is  the  same  as 
the  quality  in  that  pipe.  When  supplied  direct  from  the  boiler, 
x'  may  be  assumed  to  be  unity.  If  the  jacket  is  supplied 
through  a  reducing-valve,  the  pressure  and  quality  may  be 
determined  either  before  or  after  passing  the  valve,  since 
throttling  does  not  change  the  amount  of  heat  in  the  steam. 
Should  the  steam  applied  to  the  jacket  be  superheated  from 
any  cause,  we  may  use  the  equation 

a,=»[v+^.'-o-/i.  •  •  •  (294) 

in  which  \f  is  the  total  heat  of  saturated  steam  at  the  tempera- 
ture /',  and  txr  is  the  temperature  of  the  superheated  steam. 

Equation  (292)  furnishes  a  method  of  calculating  the  heat 
lost  by  radiation  and  conduction  ;   but  since  Qe  is  obtained  by 


312  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

subtraction  and  is  small  compared  with  the  quantities  on  the 
right-hand  side  of  the  equation,  the  error  of  this  determination 
may  be  large  compared  with  Qe  itself.  The  usual  way  of  de- 
termining Qe  for  an  engine  with  a  jacket  is  to  collect  the  water 
condensed  in  the  jacket  for  a  known  time,  an  hour  for  exam- 
ple, when  the  engine  is  at  rest,  and  then  the  radiation  of  heat 
per  hour  may  be  calculated.  If  it  be  assumed  that  the  rate 
of  radiation  at  rest  is  the  same  as  when  the  engine  is  running, 
the  radiation  for  any  test  may  be  inferred  from  the  time  of  the 
test  and  the  determined  rate.  But  the  engine  always  loses 
heat  more  rapidly  when  running  than  when  at  rest,  so  that  this 
method  of  determining  radiation  always  gives  a  result  which 
is  too  small. 

If  a  steam-engine  has  no  jacket  it  is  difficult  or  impossible 
to  determine  the  rate  of  radiation.  The  only  available  way 
appears  to  infer  the  rate  from  that  of  some  similar  engine  with 
a  jacket.  Probably  the  best  way  is  to  get  an  average  value 
of  Qe  from  the  application  of  equation  (292)  to  a  series  of  care- 
fully made  tests. 

It  is  well  to  apply  equation  (292)  to  any  test  before  begin 
ning  the  calculation  for  Hirn's  analysis,  as  any  serious  error  is 
likely  to  be  revealed,  and  so  time  may  be  saved. 

When  the  radiation  Qe  is  known  from  a  direct  determina- 
tion of  the  rate  of  radiation,  we  may  apply  Hirn's  analysis  to 
a  test  on  an  engine  even  though  the  quantities  depending  on 
the  condenser  have  not  been  obtained.  For  from  equation 
(292) 


-Mq,  -  G(qk  -  q^  =  Qt-Q-  Q.  +  A(Wa  +  Wb-Wc-  Wd\ 
and  consequently 
Qc  =  /,-/,-  Q  -  Qj+  Q.+.A(W.+  Wt-2Wc-  Wd).   (294) 


Thus  it  is  possible  to  apply  the  analysis  to  a  non-condensing 

engine  or  to  the  high-pressure  cylinder  of  a  compound  engine. 

It  is  apparent  that  the  heat  Qc,  thrown  out  from  the  walls 


INFLUENCE   OF   THE   CYLINDER    WALLS.  313 

of  the  cylinder  during  exhaust,  passes  without  compensation 
to  the  condenser,  and  is  a  direct  loss.  Frequently  it  is  the 
largest  source  of  loss,  and  for  this  reason  Hirn  proposed  to 
make  it  a  test  of  the  performance  and  perfection  of  the 
engine;  but  such  a  use  of  this  quantity  is  not  justifiable,  and 
is  likely  to  lead  to  confusion. 

The  heat  Qb  that  is  restored  during  expansion  is  supplied 
at  a  varying  and  lower  temperature  than  that  of  the  source  of 
heat,  namely,  the  boiler,  and  though  not  absolutely  wasted, 
is  used  at  a  disadvantage.  It  has  been  suggested  that  an 
early  compression,  as  found  in  engines  with  high  rotative 
speed,  warms  up  the  cylinder  and  so  checks  initial  condensa- 
tion, thereby  reducing  Qa  and  finally  Qc  also.  Such  a  storing 
of  heat  during  compression  and  restoring  during  expansion  is 
considered  to  act  like  the  regenerator  of  a  hot-air  engine,  and 
to  make  the  efficiency  of  the  actual  cycle  approach  the 
efficiency  of  the  ideal  cycle  more  nearly  than  would  be  the 
case  without  compression.  It  does  not,  however,  appear  that 
engines  of  that  type  have  exceeded,  if  they  have  equalled, 
the  performance  of  slow-speed  engines  with  small  clearance 
and  little  compression. 

Application. — In  order  to  show  the  method  of  applying 
Hirn's  analysis  the  complete  calculation  for  a  test  made  9^1  a 
small  Corliss  engine  in  the  laboratory  of  the 
Institute  of  Technology  will  be  given: 

Diameter  of  the  cylinder 8  inches. 

Stroke  of  the  piston 2  feet. 

Piston  displacement:  crank  end 0.6791  cu.  ft. 

head  end 0.7016      " 

Clearance,  per  cent  of  piston  displacement : 

crank  end 3.75 

head  end 5.42 

Boiler-pressure  by  gauge 77.4  pounds. 

Barometer 14.8       " 

Condition  of  steam,  two  per  cent  of  moisture. 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


Events  of  the  stroke  : 

Cut-off  :  crank  end 0.306  of  stroke. 

head  end. . . 0.320         " 

Release  at  end  of  stroke. 

Compression  :  crank  end 0.013  of  stroke. 

head  end 0.0391       " 

Duration  of  the  test,  one  hour. 

Total  number  of  revolutions 3692 

Weight  of  .steam  used 548  pounds. 

Weight  of  condensing  water  used.. .  14,568  " 
Temperatures : 

Condensed  steam tt  =  141°.  I  F. 

Condensing  water :  cold tt  =    S2°-9  F. 

warm tk  —    88°.3  F. 

ABSOLUTE    PRESSURES,    FROM    INDICATOR-DIAGRAMS,    AND 
CORRESPONDING    PROPERTIES    OF   SATURATED   STEAM. 


CRANK  END. 

HEAD  END. 

P 

9 

P 

u 

P 

g 

P 

u 

Cut-off 

83-6 
29.2 
I4.8 
21.8 

284.6 
217.8 

181.1 

201.5 

813.0 
864.8 
893.2 
877.4 

5.190 
13.924 
26.464 
18.344 

83-3 
31-9 
14.8 
29.8 

284.4 
222.9 
181.1 
219.0 

813.2 
860.8 
893-2 
863.9 

5.207 

12.804 
26  .  464 
13.664 

Release  

Compression.  . 
Admission...  . 

MEAN    PRESSURES,    AND    HEAT- EQUIVALENTS   OF   EXTERNAL 

WORKS. 


CRAN 

K  END. 

HEAD 

END. 

Mean  Pressures. 

Equivalents  of 
Work. 

Mean  Pressures. 

Equivalents  of 
Work. 

Admission     .... 

87  7  '- 

3060 

80  1 

A  A      C 

q  877 

°y  •  j 

47    I 

.  /i  j. 

41  <O 

Exhaust 

14    8 

I    816 

14  8 

T    RAI 

Compression  . 

18  •* 

O    O2QQ 

14.0 
21   8 

1  -°47 

VOLUMES,    CUBIC    FEET. 


CRANK  END. 

HEAD  END. 

At  cut-off, 

PO  4-  V\  •  • 

0   2-m 

o  2626 

At  release 

r*+  v\ 

O   7O46 

O  73O.6 

At  compression, 

^I+Fs 

At  admission, 

y 

o.  02  550 

0.03806 

INFLUENCE   OF   THE   CYLINDER    WALLS.  31$ 

At  the  boiler-pressure,  92.1  pounds  absolute,  we  have 

r  =  888.4,         0  =  291.7. 
The  steam  used  per  stroke  is 
548 


2  X  3692 

The  steam  caught  in  the  clearance  space  at  compression, 
on  the  assumption  that  the  steam  is  then  dry  and  saturated, 
is  obtained  by  multiplying  the  mean  volume  at  that  point  by 
the  weight  of  one  cubic  foot  of  steam  at  the  pressure  at  com- 
pression, which  is  0.03781  of  a  pound. 

0.0343  +  0.065  5 
.*.    MQ  =  -        —  —        -  X  0.03781  =0.0019  of  a  pound; 

M  -f  M0  =  0.0742  +  0.0019  =  0.0761  pound. 
The  condensing  water  used  per  stroke  is 
14568 


<2  =  M(xr  +  q)  =  0.0742(0.98  X  888.3  +  291.8)  =  86.243  ; 


J(0.02  550  +  0.03  806) 

**  A       '— 


0.0019  X  4(18.344+  13.664)      62.4 Xi(!8. 344+ 13- 
=  1.043- 

This  indicates  that  the  steam  is  superheated  at  admission. 
Such  may  be  the  case,  or  the  appearance  may  be  due  to  an 
error  in  the  assumption  of  dry  steam  at  compression,  or  to 
errors  of  observation.  It  is  convenient  to  assume  xa  =  i. 


3l6          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 
(0.2333+0.2626)  I 


* 


0.0761  x  4(5-190+  5-207)      62.4  X  4(5-i9O  +  5.207) 
=  0.6236. 


£(0.7046  -f-  0.7396) 


0.0761  x4(i  3-924+  12.804)      62.4x4(13-924+12.804) 
=  0.7088. 

70  =  M,(q,  +  *0p0)  ; 


/.  =  i  X  o.ooi9[2oi.5  +  219.0  +  1.00(877.4  +  863.9)] 
=  2.054. 


7,  =  J  X  o.o76i[284.6  +  284.4  +  0.6236(813.0  +  813.2)] 
=  60.238. 


7,  =  4  X  o.o76i[2i7.8  4-  222.0  +  0.7088(864.8  +  861.8)] 
=  63.311. 


7,  =  0.0019(181.1  +  893.2)  =  2.041. 


a  =  86.243  +  2.054  -  60.238  -  ^3.369  +  3.711)  =  24.519. 

Qb  =  7,  -7,  -AWb\ 

G*  =  60.238  -  63.311  -  4(3.877  +  4.159)  =  -  7.091. 


INFLUENCE   OF  THE   CYLINDER    WALLS.  3  1/ 

/.    Qe  =  63.311  —  2.041  —  0.0742  X  109.3 

-  1.973(56.35  -  21.01)  +  i(l-836+  1.847) 
-   I4.72L 


Qd=  2.041  —  2.054  +  K°-0299  +  °-II04)  =  0.157 


Also,  equation  (292)  for  this  case  gives 


&  =  p-  Mg-  G(qk  -  q^-AW 

=  86.243  —  8.110  —  69.723—  (3.540+4.018—  1.841—  0.070) 
=  86.243  —  8.  1  10  —  69.723  —  5.647  =  2.764. 

It  is  to  be  remembered  that  the  heat  lost  by  radiation  and 
conduction  per  stroke,  when  estimated  in  this  manner,  is 
affected  by  the  accumulated  errors  of  observation  and  com- 
putation, which  may  be  a  large  part  of  the  total  value  of  Qe. 

Dropping  superfluous  significant  figures,  we  have  in 
B.  T.  U. 

2  =  86.2,  a  =  24.5,         <2*=-7-i,         *£y 

a  =-14-7,     a  =  .o6,      Q.  =  2.8. 

The  horse-power  of  the  engine  is 

t' 
778  X  5^47  X  3692  X2 

60X33000  16.35  H.P., 

and  the  steam  per  horse-power  per  hour  is 

548 


16.35 


=  33-5  pounds. 


The  data  and  results  for  this  test  and  for  four  others  made 
at  the  same  time  are  given  in  Table  II. 


318 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


TABLE  II. 

APPLICATION  OF  HIRN'S  ANALYSIS  TO  A  SMALL  CORLISS  ENGINE  AT  THE  MASSACHUSETTS 
INSTITUTE  OF  TECHNOLOGY. 

DIAMETER,  8  INCHES;  STROKE,  24  INCHES. 

Absolute  pressures,  pounds. 

Admission. 

A 

M 

BQ 

oo  t>.  0*00  oo 
O  10  -<i-  ^i-  o 

MN    «    CON 

•spunod 
'anoq  J3d  J3A\od 
-asjoq  J3d  uiBajg 

fn\O   O   ro  10 

*%Jsa 

M 

u 

00    t^  t>OO  00 

1 

!^ 

^: 

rt  03 

a 

w 
c 

•J3MOd-3SJOq 

pajBoipuj 

£0*0  fi.  i?S 

VO  CO  00    M  VO 

•JOJJ3         ^ 
PUB  UOllBlpB^^ 

"i  ro  N  oo  vo 
vo  in  n-  ro  t^ 

N    M    ci    M  N 

g 

« 

as 

oo  t^  ooo  oo 

Compressi 

/3 

•uoisssjduioo 
Suunp  SHBA\    ^ 
Aq  paqjosqy 

SPJ?^^ 

6    0    0    0    0 

w 
u 

00^0000 

•}snBqx3 
5uunp  SJJBM    Q^ 
^q  pappiA 

•*  N    t>>  •*-  tv 
VO    ON  t^.  O\  •*• 

Release. 

/a 

w 
pa 

oo  t^  rooo  o 
vd   ON  O   ro  M 

•uoisuBdxa 
SuunpsfiBM    Q^ 
/iq  pappiA 

^^° 

CJ      M      M      0      t^. 

M 

J 

ro  txvo  oo  e» 
vd  t^.oo  M  o\ 

•UOISSIUIpB 
J§UUtipS[lBM       f^3 

Aq  paqjosqy 

M^OOO    O^C^ 

8  S  5  ??  JT 

i< 

u 

W 
ffi 

ro  t^  10  m  to 

vd  fi  t^-  d  co 

t^OO    t^OO  CO 

•njcais^siom 
jo  spunod    Oi 

W  Ul  1B3H 

SvSvgSct 

iri  w    r^  -^-VO 
^  10  u-)VO  oo 

M 

d 

M    t>.  N    H  VO 

snts  of  work. 
.  U. 

Com- 
pression. 

AWd 

H 
BE 

Is  f"2  2 

d  d  o  6  d 

t"x  CO  -^  t**  CO 

t^oo  t~-  t^oo 

W 
CJ 

o 

C4    IO  W    O  O 

!??g  ?S 

•spunod  '38nv3      ^ 
A"q  aunssajd-aaijog 

VO    t>.VO    tx  tx 

Exhaust. 
AWC 

H 
E 

ro  O  00    ^  t^. 
t^oooo  oo"oo" 

•qoui  ajnnbs  aqj  uo 
spunod  'aaiaaioJBg 

OO    t>-  OvOO  00 

?2"?^2" 

M 

cj 

§££&£ 

Temperatures, 
degrees  Fahrenheit. 

•UJJBM  'J3JBAA.          ^ 

-Suisuapuo3  "** 

CO  0    O  OO    CO 
t^OO    t^  COOO 

Heat-equival 
E.  T 

Expansion. 
AWb 

« 
B 

•^-  ro  -^-  o  O 

03  C»^VO    N     if} 

•p[OD  '43JBM         .w 

-Suisuapuo^  "** 

<N  OO    (M  VO    O> 

d>  TJ-  ^  co  ci 
co  to  co  in  in 

K 
U 

Admission. 
AWa 

M 

ffi 

sss^s 

•WB3JS          ^ 

pasu»puo3  "** 

vo  m  o  oo  M 
oo  O^oo  e^  M_ 

O    M    M    N    M 

H 

U 

t^    U~J    M  OO     O 

CM    O    t^  o  vO 
H    M   hi    CM    ro 

•UIB3JS  UI         ^ 
SuiUJUd  JO  }U3D  J3J     1 

ci  w  ci  w  ei 

Events  of  the  stroke— 
per  cent  of  stroke  from  beginning. 

iJ 

n'uj 

O  in 

0  u 

a 

w 
.    as 

t-.vo  -*oo 

t^^-fO'i-ro 

•spunod  'jsiBM-Hui 
-suapuoo  jo  iqSpM. 

m  t>.  o\oo  vo 

00    O    £N  00    10 
CO  0    ^00    Jj- 

M 

U 

W     ~     0     M     M 

Release. 

bf 

0    0    Q    0    0 

•spunod  'pasn 
meals  jo  ;q3p^V 

co  i-^.  o  inoo 
S-co^^S 

bd 

u 

88888 

•suonnjoAaj 
jo  jaqiunu  prjoj^ 

3o*8?l£ 

00  vo  00  vo  vo 

Cut-off. 

M 
DC 

0    N    0   in  0 
(>  N   »r;  Ov  IN 

•sajnuira  'uopBjna 

&£&3v8 

w 
u 

0   (N   0   mvo 
O   N   in  o\  O 

•-wquirix               -?,<x*f*3 

uaqumN      |    ^ftlC9^u9 

INFLUENCE    OF   THE   CYLINDER    WALLS.  319 

Effect  of  Varying  Cut-off. — An  inspection  of  the  inter- 
changes of  heat  show  that  the  values  of  Qa,  the  heat  absorbed 
by  the  walls  during  admission,  increases  regularly  as  the  cut- 
off is  lengthened,  and  that  the  heat  returned  during  expansion 
decreases  at  the  same  time  so  that  there  is  a  considerable 
increase  in  the  value  of  the  heat  Qc  which  is  rejected  during 
exhaust.  Nevertheless  there  is  a  large  gain  in  economy  from 
restricting  the  cut-off  so  that  it  shall  not  come  earlier  than 
one-third  stroke.  Unfortunately  tests  on  this  engine  with 
longer  cut-off  than  one-third  stroke  have  not  been  made,  and 
consequently  the  poorer  economy  for  long  cut-off  cannot  be 
shown  for  this  engine  as  for  the  engine  of  the  Michigan. 

Hallauer's  Tests. — In  Table  III  are  given  the  results  of 
a  number  of  tests  made  by  Hallauer  on  two  engines,  one 
built  by  Him  having  four  flat  gridiron  valves,  and  the  other 
a  Corliss  engine  having  a  steam-jacket.  Two  tests  were  made 
on  the  former  with  saturated  steam  and  six  with  superheated 
steam.  Three  tests  were  made  on  the  latter  with  satu- 
rated steam  and  with  steam  supplied  to  the  jackets.  These 
tests  have  a  historic  interest,  for  though  not  the  first  to  which 
Hirn's  analysis  was  applied,  they  are  the  most  widely  known, 
and  brought  about  the  acceptance  of  his  method.  They  have 
also  a  great  intrinsic  value,  as  they  exhibit  the  action  of  two 
different  methods  of  ameliorating  the  effect  of  the  action  of 
the  cylinder  walls,  namely,  by  the  use  of  superheated  steam 
and  of  the  steam-jacket.  In  all  these  tests  there  was  little 
compression,  and  Qd>  the  interchange  of  heat  during  compres- 
sion, is  ignored. 

Superheated  Steam. — Steam  from  a  boiler  is  usually 
slightly  moist,  x,  the  quality,  being  commonly  0.98  or  0.99. 
Some  boilers,  such  as  vertical  boilers  with  tubes  through  the 
steam  space,  give  steam  which  is  somewhat  superheated,  that 
is,  the  steam  has  a  temperature  higher  than  that  of  saturated 
steam  at  the  boiler-pressure.  Strongly  superheated  steam  is 
commonly  obtained  by  passing  moist  steam  from  a  boiler 


320  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


W 


O 

.   u 


m 


•33|OJ1S  jad                   v. 

paioafaj  -fl  'X  '8      ^ 

r>.  o* 

M     M 

\n  o  O   M  t~>  r-x 

t^  r^o  oo  cx>    i 

555 

Exchanges  of  heat  in  percent  of  total 
heat  furnished  per  stroke. 

It1 

:::::: 

M    OMH 

vo  4  4 

<^ 

»o  O 

o    ;  c»  coo    ) 

M        •     M     M     M       • 

XO 

O  en  M 

or 

0     Tl- 

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«     M 

m  r^oo  if>  c*  °J 
w  ON  rA  o  ^  *p 

M                      M     M      | 

enoo  O 

N    O^OO 
M 

<5 

O   en 

n-  •  o    •    •    • 

XO    O     Tf 

u->  r^ 

CO       .    W              .       . 

i^  xo  O 

M    M   M 

d? 

to  O» 

n-   .  o 

"t  M    rt 

O*     M    VO 
«    N     M 

CO    CO                N       .     >-> 
N    W                N      .    M             .       . 

1 

•sinuitn  jad 

•j-H  jsd-n-jL'al 

^  a. 

'»n  Q^ 
en  co 

O   "•>  O   >->   O 
CT-  O  o>   ^oo 

N    N    CO  CO  CO     I 

•spunod  'jnoq  jad 

•J'H  J3d  UIBaJS 

O^  Ml 

a*  N 

O    1^.  W    N    N    ON 

oo  r^oo 

O  *^>  i^*  oo  o  f^     i      i^  r^«  i"^ 

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rfvO 

O    O   'I-  u^O   en 

O     M     O> 

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1-1  co  Tt  N  oo  r* 

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•sqi 
'ajnjosqB  ajnssajd-jpBg 

O   N 

r^  t^  M  r^  \n    ' 

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en  xn 

N  cs  xo  N  es    • 

•tpui  ajBnbs  jad 
•sq'i  'amiosqB 
ajnssajd-jaiiog 

t^  0 

MQO  ^ro  N 

RS 

M    M    O^CO    M    N 
r^  i^o  O  r>»o 

•suoisuBdxg 

M     0 

o  co 

M  i^  o^  N   N   m 
o'  -3-  en  ci  ci  en 

W  CO  O 

•ainuiui  jad 
suormjoAay 

-to 

O   O   M   en  M   o 

n-  M  en 

6  o" 

co  co 

060666 
en  en  co  en  co  co 

O   1-1   0^ 
xo  xo  rt1 

uqBji 
'tnuais  pajTjaqjadns 
jo  ajnjEjadtuax 

co  O^co   co  oo  oo 

00    M    Tf  CO  M    N 

en  rf  Tf  rt  rt  rf 

•uoijipuoo 

i 

p3TB3HJ9dns 

p3132lDBf 

«*M 

so  ^  w»  «e  i>-  QC 

OSO^ 
rH?H 

INFLUENCE   OF   THE   CYLINDER    WALLS.  321 

through  a  coil  of  pipe,  or  a  system  of  piping,  which  is  exposed 
to  hot  gases  beyond  the  boiler. 

Superheated  steam  may  yield  a  considerable  amount  of 
heat  before  it  begins  to  condense ;  consequently  where  super- 
heated steam  is  used  in  an  engine  a  portion  of  the  heat 
absorbed  by  the  walls  during  admission  is  supplied  by  the 
superheat  of  the  steam  and  less  condensation  of  steam  occurs. 
This  is  very  evident  in  Dixwell's  tests  given  by  Table  XXVII, 
on  page  371,  where  the  water  in  the  cylinder  at  cut-off  is 
reduced  from  52.2  percent  to  27.4  percent,  when  the  cut-off 
is  two-tenths  of  the  stroke,  by  the  use  of  superheated  steam; 
with  longer  cut-off  the  effect  is  even  greater.  This  reduction 
of  condensation  is  accompanied  by  a  very  marked  gain  in 
economy. 

The  way  in  which  superheated  steam  diminishes  the  action 
of  the  cylinder-walls  and  improves  the  economy  of  the  engine 
is  made  clear  by  Hallauer's  tests  in  Table  III.  A  comparison 
of  tests  I  and  3,  having  six  expansions,  shows  that  the  heat 
Qa  absorbed  during  admission  is  reduced  from  28.3  to  22.4 
per  cent  of  the  total  heat  supplied,  and  that  the  exhaust  waste 
is  correspondingly  reduced  from  21.6  to  12.5  per  cent.  A 
similar  comparison  of  tests  2  and  5,  having  nearly  four  expan- 
sions, shows  even  more  reduction  of  the  action  of  the  cylinder- 
walls.  The  effect  on  the  restoration  of  heat  Qb  "during 
expansion  appears  to  be  contradictory:  in  one  case  there  is 
more  and  in  the  other  case  less.  It  does  not  appear  profitable 
to  speculate  on  the  meaning  of  this  discrepancy,  as  it  may  be 
in  part  due  to  errors  and  is  certainly  affected  by  the  unequal 
degree  of  superheating  in  tests  3  and  5.  It  may  be  noted 
that  the  actual  value  of  Qc  in  calories  is  nearly  the  same  for 
tests  I  and  2,  there  being  a  small  apparent  increase  with  the 
increase  of  cut-off,  which  is,  however,  less  than  the  probable 
error  of  the  tests.  The  exhaust  waste  Qc  is  much  more 
irregular  for  tests  3  to  7  for  superheated  steam.  The  in- 
crease from  8 1  to  87  B.  T.  U.  from  test  6  to  test  7  may 
properly  be  attributed  to  a  less  degree  of  superheating;  the 


322  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

increase  from  66  to  81  B.  T.  u.  for  tests  5  and  6  is  due  to 
longer  cut-off  and  less  superheating;  finally,  the  steady  reduc- 
tion from  75  to  66  B.  T.  U.  for  the  three  tests  3,  4,  and  5  is 
probably  due  to  the  rise  of  temperature  of  the  superheated 
steam,  which  more  than  compensates  for  the  effect  of 
lengthening  the  cut-off.  Finally,  in  test  8  the  exhaust  waste 
is  practically  reduced  to  zero  by  the  use  of  strongly  super- 
heated steam  in  a  non-condensing  engine;  this  shows  clearly 
that  the  exhaust  waste  Qc  by  itself  is  no  criterion  of  the  value 
of  a  certain  method  of  using  steam. 

Steam-jackets. — If  the  walls  of  the  cylinder  of  a  steam- 
engine  are  made  double,  and  if  the  space  between  the  walls  is 
filled  with  steam,  the  cylinder  is  said  to  be  steam-jacketed. 
Both  barrel  and  heads  may  be  jacketed,  or  the  barrel  only 
may  have  a  jacket;  less  frequently  the  heads  only  are 
jacketed.  The  principal  effect  of  a  steam-jacket  is  to  supply 
heat  during  the  vaporization  of  any  water  which  may  be  con- 
densed on  the  cylinder-walls.  The  consequence  is  that  more 
heat  is  returned  to  the  steam  during  expansion  and  the  walls 
are  hotter  at  the  end  of  exhaust  than  would  be  the  case  for 
an  unjacketed  engine.  This  is  evident  from  a  comparison  of 
tests  I  and  1 1  in  Table  III.  In  test  I  only  a  small  part  of  the 
heat  absorbed  during  admission  is  returned  during  expansion, 
and  by  far  the  larger  part  is  wasted  during  exhaust.  In  test 
1 1  the  heat  returned  during  expansion  is  equal  to  two-thirds 
that  absorbed  during  admission,  though  a  part  of  this  heat  of 
course  comes  from  the  jacket.  About  half  as  much  is  wasted 
during  exhaust  as  is  absorbed  during  admission.  The  con- 
densation of  steam  is  thus  reduced  indirectly:  that  is,  the 
chilling  of  the  cylinder  during  expansion,  and  especially  during 
exhaust,  is  in  part  prevented  by  the  jacket,  and  consequently 
there  is  less  initial  condensation  and  less  exhaust  waste,  and 
in  general  a  gain  in  economy.  But  though  there  are  many 
tests  of  engines  both  with  and  without  steam  in  the  jackets, 
there  is  so  much  diversity  of  results  that  engineers  are  not 
.agrted  as  to  the  conditions  under  which  it  is  profitable  to  use 


INFLUENCE   OF   THE   CYLINDER    WALLS.  323 

a  steam-jacket,  nor  as  the  amount  of  gain  to  be  expected 
under  a  given  set  of  conditions. 

The  jacket  on  the  cylinder  of  a  simple  engine  is  usually 
supplied  with  steam  from  the  main  supply-pipe,  so  that  the 
pressure  in  the  jacket  is  little  if  any  more  than  that  in  the 
cylinder  during  admission.  As  the  steam  in  the  cylinder 
comes  in  direct  contact  with  the  inner  surface  of  the  walls, 
while  the  jacket  steam  is  in  contact  with  the  outer  surface  of 
the  walls,  the  heat  absorbed  by  the  walls  during  admission 
comes  mainly  if  not  entirely  from  the  steam  in  the  cylinder. 
It  is  probable  that  the  action  is  much  the  same  when  the 
pressure  in  the  jackets  is  higher  than  that  of  the  steam  which 
is  supplied  to  the  cylinder,  as  is  the  case  when  full  boiler- 
pressure  is  let  into  the  jacket  of  the  low-pressure  cylinder  of 
a  compound  engine.  Now  the  heat  supplied  during  expan- 
sion, though  it  does  some  work,  is  first  subjected  to  a  loss  of 
temperature  in  passing  from  the  steam  in  the  jacket  to  the 
cooler  water  on  the  walls  of  the  cylinder,  and  such  a  non- 
reversible  process  is  necessarily  accompanied  by  a  loss  of 
efficiency.  On  the  other  hand,  the  heat  supplied  by  a  jacket 
during  exhaust  passes  with  the  steam  directly  into  the 
exhaust-pipe.  It  appears,  then,  that  the  direct  effect  of  a 
steam-jacket  is  to  waste  heat;  the  indirect  effect  (drying 
and  warming  the  cylinder)  reduces  the  initial  condensation 
and  the  exhaust  waste  and  often  gives  a  notable  gain  in 
economy. 

Application  to  Multiple-expansion  Engines. — The  ap- 
plication of  Hirn's  analysis  to  the  high-pressure  cylinder  of  a 
compound  or  multiple-expansion  engine  may  be  made  by 
using  equations  (279),  (280),  and  (282)  for  calculating  Qa>  Q6, 
and  Qdy  while  equation  (294)  may  be  used  to  find  Qc. 

A  similar  set  of  equations  may  be  written  for  the  next 
cylinder,  whether  it  be  the  low-pressure  cylinder  of  a  com- 
pound engine  or  the  intermediate  cylinder  of  a  triple  engine, 
provided  we  can  determine  the  value  of  Q',  the  heat  supplied 
to  that  cylinder.  But  of  the  heat  supplied  to  the  high-pres- 


324 


THERMODYNAMICS   OF    THE   STEAM-ENGINE. 


TABLE  IV. 

APPLICATION  OF  HIRN'S  ANALYSIS  TO  THE  EXPERIMENTAL 
ENGINE  AT  THE  MASSACHUSETTS  INSTITUTE  OF  TECH- 
NOLOGY. 

COMPOUND;  CYLINDER  DIAMETERS,  9  AND  24  INCHES;  STROKE,  30  INCHES. 
Technology  Quarterly,  vol.  XI,  p.  43. 


Test  numbers. 

I. 

II. 

in. 

IV. 

Duration  of  test   minutes  

60 

60 

60 

60 

4882 

Revolutions  per  minute  
Steam-consumption  during  test,  pounds: 
Passing  through  cylinders  
Condensation  in  h   p  jacket  .... 

82.93 
844-5 

82.QO 
820.0 

81.72 
1050.0 

81.37 

1086.  o 

"             in  receiver  jacket  

80.0 

"             in  1   p.  jacket  

82  8 

88  <; 

88  o 

Total        

1006  8 

08=  o 

Condensing  water  for  test,  pounds  

16066 
I  0# 

16287 

21800 

21960 

Temperatures,  Fahrenheit: 

86  o 

loc.  8 

Pressure  of  the  atmosphere,  by  the  barometer, 
pounds  per  square  inch               
Boiler-pressure,  Ibs.  per  sq.  in.,  absolute  
Vacuum  in  condenser,  inches  of  mercury  
Events  of  the  stroke,  per  cent: 
High-pressure  cylinder  — 

!4-5 
114.7 
26.6 

16.8 

'4-5 
"5-5 
26.6 

ic  g 

14-5 

"5-4 
26.3 

27    8 

14-5 
"5-9 
26.3 

head  end  
Release   both  ends 

i5-7 

I5-4 

24.2 

25.2 
25-6 

Compression,  crank  end  
head  end  ....                  ... 

7-5 
n*5 

7-5 

7-5 

7-5 

Low-pressure  cylinder  — 
Cut-off  crank  end        ..     .          ...> 

18.0 

l8.O 

18.0 

18  o 

Release  both  ends  

IOO.O 

Absolute  pressures  in  the  cylinder,  pounds 
per  square  inch: 
High-pressure  cylinder— 

head  end  .  .          

107.  i 

108  i 

29.9 

78    2 

headend  

24.7 

24.8 

18  o 

18  7 

17   8 

Admission   crank  end               .... 

06.  c 

08    2 

* 

Low-pressure  cylinder  — 

headend    

13.6 

X3*9 

Release   crank  end          

Compression   crank  end  

1  .9 

2    8 

5.8 

Heat-equivalents  of   external  work,  B.  T.  u. 
from  areas  on  indicator-diagram  to  line  of 
absolute  vacuum: 
High-pressure  cylinder— 
During  admission,  A  Wa,  crank  end.... 
head  end  

3-59 

3-49 

3.38 
3.47 

5-i3 
5*43 

EC 

INFLUENCE   OF   THE   CYLINDER    WALLS. 
TABLE  IV — Continued. 


325 


Test  numbers. 


II. 


High-pressure  cylinder— 

During  expansion,  A  Wb,  crank  end....  7-( 

headend —  7.1. 

During  exhaust,  A  We,  crank  end 2.86 

head  end 2.91 

During  compression,  A  Wd,  crank  end  0.35 

head  end.  0.67 
Low-pressure  cylinder — 

During  admission,  A  Wa,  crank  end.. .  4.13 

head  end  ...  4.07 

During  expansion,  A  Wb,  crank  end ...  7. 19 

head  end 7.05 

During  exhaust,  A  We,  crank  end 2.64 

head  end 3.25 

During  compression,  A  Wd,  crank  end..  0.12 

head  end  ..  0.33 

Quality  of  the  steam  in  the  cylinder.     At  ad- 
mission and  at  compression  the  steam  was 
assumed  to  be  dry  and  saturated: 
High-pressure  cylinder— 

At  cut-off xl   70.18 

Atrelease JT, 83.98 

Low-pressure  cylinder— 

At  cut-off a-j 91 .94 

Atrelease ...r, 87.62 

Interchanges  of  heat  between  the  steam  and 
the  walls  of  the  cylinders,  in  B.  T.  u. 
Quantities  affected  by  the  positive  sign  are 
absorbed  by  the  cylinder-walls;  quantities 
affected  by  the  negative  sign  are  yielded 
by  the  walls: 

High-pressure  cylinder — 

Brought  in  by  steam Q 99-82 

During  admission     .....Qa 25.22 

During  expansion   Qb —15.01 

During  exhaust Qc —11.13 

During  compression Qd 0.98 

Supplied  by  jacket Of 3.70 

Lost  by  radiation Qe 1.87 

Second  intermediate  receiver- 
Supplied  by  jacket Qr 3.30 

Lost  by  radiation..  ...  ..Qre 0.69 

Low-pressure  cylinder — 

Brought  in  by  steam Q* 96.24 

During  admission   Q*a 7.63 

During  expansion   ....... cX* —  1.75 

During  exhaust Q'c — n.n 

During  compression Q'd o.  33 

Supplied  by  jacket   ..    ..Q'j 7.30 

Lost  by  radiation   O/e 4.44 

Total  loss  by  radiation: 

By  preliminary  test "ZQt  7.39 

By  equation 7.00 

Power  and  economy: 

Heat-equivalents  of  works  per  stroke: 

High-pressure  cylinder..^  W 8.02 

Low-pressure  cylinder. .  .A  W 8.10 


Totals   


Total  heat  furnished  by  jackets 

Distribution  of  work: 

High-pressure  cylinder 

Low-pressure  cylinder 

Total  horse-power 

Steam  per  horse-power  per  hour  

B.  T.  U.  per  horse-power  per  minute 


16.12 

14-30 

i  .00 

I. 01 

63.07 
15.96 
282.1 


8.05 

7-97 
2.96 

3-°3 
0.37 
0.72 

4.15 
4-13 
7-25 
7.12 
2-55 
3-io 
0.13 
0.32 


71.11 

BS-59 


95.20 
88.19 


97.10 

23-85 

-15.84 

-10.04 

o  45 

3-45 

1.87 

0.69 

94.26 
5-44 

-  1. 12 

-  7-53 
2.21 
6.56 

4-44 


7.89  , 

8.27   I 


IV. 


8.38 
8.48 

3-" 
3-18 
0.38 
o  72 

5-93 
5-Q9 
7.78 
7.88 
2.87 
3-98 
0.17 
0.28 


73.60 
84.97 

92-13 
88-57 


126.90 

27.14 

—  16.13 

—12.99 

0.46 


1 .00 

123.40 

9-63 

-  2.03 

—  9.92 

O.II 

7.91 
5.70 


10.01 

10.04 


IV. 


16.16 
14-54 


1.05 
63.19 
15-59 
275-1 


20.05 
18.22 

I.OO 
1. 00 

5:3 

284.4 


8-43 
8.57 
3-28 
3-54 
0.40 
0.72 

6. n 
6.25 
7-99 
8.16 
2.98 
4.00 
0.17 
0.29 


76.24 
83-73 

92.58 
87.86 


131.30 

25'^ 
—  12.60 

-15-47 
0.47 
3-97 

2.20 


7.19 
I.  60 

128.53 

I0>57 

—0.97 

-16.53 

0.64 

7.85 

5.70 

9.52 
4-42 


10.17 
10-53 


20.70 
19.01 

I.OO 

1.04 

80.47 

16.14 
283.8 


326  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

sure  cylinder  a  part  is  changed  into  work,  a  part  is  radiated,. 
and  a  part  is  rejected  in  the  exhaust  waste.  The  heat  rejected 
is  represented  by 

J-AW-Q,,  ,  "•"*".!.  "•  (295) 


where  Q  is  the  heat  supplied  by  the  steam  entering  the 
cylinder,  Qj  is  the  heat  supplied  by  the  jacket,  AW  is  the 
heat-equivalent  of  the  work  done  in  the  cylinder,  and  Qe  is 
the  heat  radiated.  Suppose  the  steam  from  the  high-pressure 
cylinder  passes  to  an  intermediate  receiver,  which  by  means 
of  a  tubular  reheater  or  by  other  means  supplies  the  heat  QrJ 
while  there  is  an  external  radiation  Qre.  The  heat  supplied 
to  the  next  cylinder  is  consequently 

0  =  Q  +  Qj-AW-Q.+  Qr-  Qrt.  .     .     (296) 

In  a  like  manner  we  may  find  the  heat  Q"  supplied  to  the 
next  cylinder;  for  example,  to  the  low-pressure  cylinder  of  a 
triple  engine. 

It  is  clear  that  such  an  application  of  Hirn's  analysis  can 
be  made  only  when  the  several  steam-jackets  on  the  high-  and 
the  low-pressure  cylinders,  and  the  reheater  of  the  receiver, 
etc.,  can  be  drained  separately,  so  that  the  heat  supplied  to 
each  may  be  determined  individually. 

Table  IV  gives  applications  of  Hirn's  analysis  to  four  tests 
on  the  experimental  engine  in  the  laboratory  of  the  Massa- 
chusetts Institute  of  Technology,  using  the  high-  and  low- 
pressure  cylinders  only  as  a  compound  engine. 

Table  V  gives  application  to  four  tests  on  the  same  engine 
running  as  a  triple  engine. 

It  will  be  noted  that  in  both  sets  of  tests  the  steam  in  the 
cylinders  becomes  drier  in  its  course  through  the  engine, 
under  the  influence  of  thorough  steam-jacketing  with  steam 
at  boiler-pressure.  In  the  triple-expansion  tests  the  steam  is 
practically  dry  at  release  in  the  low-pressure  cylinder.  All  of 
the  tests  show  superheating  in  the  low-pressure  cylinder, 
which  is  of  course  possible,  for  the  steam  in  the  jackets  is  at 


INFLUENCE   OF   THE    CYLINDER    WALLS. 


327 


TABLE  V. 

APPLICATION  OF  HIRN'S  ANALYSIS  TO  THE  EXPERIMENTAL 
ENGINE  IN  THE  LABORATORY  OF  THE  MASSACHUSETTS 
INSTITUTE  OF  TECHNOLOGY. 

TRIPLE-EXPANSION;  CYLINDER  DIAMETERS,  9,  16,  AND  24  INCHES  ; 

STROKE,  30  INCHES. 
Trans.  Am.  Soc.  Mech.  Engrs.,  vol.  XII,  p.  740. 


I. 

II. 

III. 

IV. 

60 

60 

60 

60 

Total  number  of  revolutions  
Revolutions  per  minute 

5299 

88.  ^ 

5228 
87  I 

5173 

86  2 

5148 

8*.  8 

Steam-consump'n  during  test,  Ibs.  : 
Passing  through  cylinders  
Condensation  in  h.  p.  jacket.. 
"    in  first  receiver-  jacket 
'    in  inter,  jacket  
"    in  sec'd  receiver-jacket 
"    in  1   p    jacket   

"93 

57 
61 

85 
53 
8q 

"57 
50 
64 
92 
50 
76 

1234 

A9 
69 

97 

52 
QO 

1305 
30 
72 
105 
51 
87 

Total 

icog 

1480 

IC.7I 

i6c.o 

Condensing  water  for  test,  Ibs.  .  . 
Priming   by  calorimeter 

22847 

O  OI^ 

22186 

O  OI2 

20244 
O   OI  I 

20252 

O   OI2 

Temperatures,  Fahrenheit: 
Condensed  steam  

Q5.4 

Q2.  I 

102.4. 

IOC    a 

41  .Q 

42.  I 

40.0 

42   8 

Condensing-  water,  hot  
Pressure  of  the  atmosphere,  by  the 

96.i 
14.8 

96.6 
14-8 

106.3 

14.7 

109.6 
14    7 

Boiler  pressure,    Ibs.    per  sq.    in. 
absolute          

ICC  .  9 

JCC.  C     . 

1  56   Q 

I  C7    7 

Vacuum    in    condenser,  inches  of 

2C  .0 

oe    I 

24    I 

oa    Q 

Events  of  the  stroke  : 
High-pressure  cylinder  — 
Cut-off   crank  end     .        . 

0.  1  02 

O    IQ4 

O    24  C. 

-^j.y 
O   '  83 

head  end.  ........ 
Release   both  ends 

0.215 
I    OO 

0.205 
I    OO 

O.27I 
I    OO 

o.;os 

I    OO 

Compression,  crank  end., 
head  end.  .  . 
Intermediate  cylinder  — 
Cut-off   both  ends          .  .  .  . 

0.05 
0.05 

O    2Q 

O.O5 
0.05 

O    2Q 

0.04 
O.O5 

o  29 

0.04 

0.05 

o  29 

Release    both  ends     

I    OO 

I    OO 

I    OO 

I    OO 

Compression,  crank  end.  . 
head  end...  . 
Low-pressure  cylinder  — 
Cut-off   crank  end                • 

O.O3 
O.O4 

o  ^8 

0.03 
0.04 

o  38 

o  03 
0.04 

o  38 

0.03 
0.04 

o  38 

head  end       •       • 

O    3Q 

OQQ 

O'lQ 

O-5Q 

I.OO 

i  oo 

I   OO 

I    OO 

328  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

TABLE  V — Continued. 


I. 

II. 

III. 

IV. 

Absolute  pressures   in   the  cylin- 
der, pounds  per  sq.  in.: 
High-pressure  cylinder  — 
Cut-off    crank  end 

TIE      O 

138  8 

i  "^8   i 

head  end                . 

I  4  "3    2 

1  4^      I 

1  40  ^ 

140  6 

Release,  crank  end  

41    ^ 

41    ^ 

44    7 

48  4 

head  end 

41    ^ 

4O    ^ 

_1  c     7 

4Q    S 

Compression,  crank  end... 
head  end..  .  . 
Admission   crank  end    .    • 

43-7 
48.7 

6/1  c 

45-3 
47-9 
68  8 

48-5 

54-5 

72    2 

53-2 
62.0 

8l    2 

head  end  .  4  .  .  . 

7<r    o 

74   8 

86  7 

O7    8 

Intermediate  cylinder  — 

37    2 

•?7.6 

38.6 

4O   Q 

head  end           .... 

oc    o 

qe  .  o 

•JQ  5 

42    6 

Release    crank  end  

iq  6 

14   2 

14    7 

16  o 

head  end 

ro     A 

jq      8 

14    O 

16  o 

Compression,  crank  end... 
head  end  — 
Admission,  crank  end.   .  .  . 

I6.3 

17.9 
20.  4 

17-3 

18.8 
20.  8 

18.2 

20.3 

22    2 

19.0 

22.4 

2a    i 

head  end  
Low-pressure  cylinder  — 
Cut-off,  crank  end     

21.  1 
12.  1 

22.8 
12   6 

24.2 
12    4 

26.7 

1-5      2 

12.  0 

12  .4 

iq  .  i 

M.  O 

Release   crank  end      

n  6 

C  .-1 

51 

57 

head  end    

c  .4 

<;  8 

e    Q 

6   4 

Compression  and  admission  — 
crank  end       

37 

T  8 

4T 

42 

4..  3 

4c 

4   6 

47 

Heat-equivalents  of  external  work, 
B.  T.  u.  ,  from   areas  on  indica- 
tor-diagram to  line  of  absolute 
vacuum: 
High-pressure  cylinder  — 
During  admission, 
A  IV  a    crank  end  

e  .71 

«;  78 

7OO 

8  lo 

head  end     ...... 

6  61 

6  •?? 

8  42 

9    en 

During  expansion, 
A  Wbt  crank  end  

10.65 
10.81 

10.76 

u  .04 

10.40 

II  .22 

10.25 
II  .OQ 

During  exhaust, 

7.  T\ 

7   80 

8    44 

9    O2 

head  end    .  .  . 

8  08 

/  -UV 

8  i* 

9  66 

During  compression, 

0.48 

0.60 

O   4Q 

o  ^o 

o  62 

o  64 

07-2 

o  81 

Intermediate  cylinder  — 
During  admission, 
AWa     crank  end  

7  «;8 

707 

7    Qg 

8  64 

7.4-3 

7.  %,*> 

8  46 

9IO 

During  expansion, 
A  IVb'   crank  end  

9.  CA 

9C.A 

9O.I 

10  64 

Q.22 

991 

IO    37 

1  1    14 

INFLUENCE   OF    THE   CYLINDER    WALLS. 

TABLE  V — Continued. 


329 


I. 

II. 

III. 

IV. 

Intermediate  cylinder  — 
During  exhaust, 
A  We  crank  end  

Q  27 

9.4.7 

Q.64 

10.54. 

0.27 

0.47 

IO.I8 

10.84 

During  compression, 
A  IVd    crank  end  

O.  -IQ 

O.43 

O.  57 

0.46 

o  60 

O  7O 

o  78 

o  84 

Low-pressure  cylinder  — 
During  admission, 
A  Wd'  crank  end 

7  75 

7QC 

8  w 

8  Q7 

head  end        .... 

7.QQ 

8  IQ 

8.66 

Q  an 

During  expansion, 
^  IVi!'   crank  end  

6  83 

7  IO 

6  86 

7  45 

head  end     

6  87 

7.12 

7.34 

7.87 

During  exhaust, 
A  IVc"   crank  end        •    .  . 

5  08 

5  08 

4  62 

C.OQ 

5  08 

5  16 

4.81 

e  OO 

During  compression, 
A  Wd"   crank  end 

o  oo 

O  OO 

o.oo 

O  OO 

head  end  .... 

o  oo 

o  oo 

o.oo 

O  OO 

Quality  of  the  steam   in  the  cylin- 
der.    At  admission  and  at  com- 
pression the  steam  was  assumed 
to  be  dry  and  saturated  : 
High-pressure  cylinder  — 
At  cut-off     .        x\ 

o  785 

o  784 

0.848 

o  875 

At  release  x*.  . 
Intermediate  cylinder  — 
At  cut-off  .  .  tXi    . 

0.899 

o  800 

0.903 

O  QI2 

0.920 
o  co6 

0.931 

o  008 

At  release   x*  '.  . 
Low-pressure  cylinder  — 
At  cut-off.  x\"  , 

0.994 

o  078 

superheated. 

superheated. 
O  Q7O 

superheated. 
O  O74 

At  release                        x*r 

Interchanges  of  heat  between  the 
steam  and  the  walls  of  the  cylin- 
ders,  in    B.    T.    U.       Quantities 
affected  by  the  positive  sign  are 
absorbed  by  the  cylinder-walls 
quantities  affected  by  the  nega- 
tive  sign    are   yielded    by   the 
walls  : 
High-pressure  cylinder  — 
Brought  in  by  steam  .  .Q. 
During  admission     .  .    Oa 

132.93 

130.77 

I4I.II 

149.84 

During  expansion  (?$.. 
During  exhaust.  .....  .Q   . 

*$•  54 

-  18.69 

—  8  36 

^J-4J 
—  19.28 
7   22 

*/-49 
-  15-33 

•7    fQ 

14-9J 
-  14  03 

2  iS 

During  compression  .  .  .  Qd  . 
Supplied  by  jacket  .  .  .  .  Qj.  . 
Lost  bv  radiation  Qe. 

0.45 
4-56 

ICQ 

0.51 
4.08 
112 

0.49 

2-39 

I    54 

0.52 
2.50 
I   54 

First  intermediate  receiver  — 
Supplied  by  jacket  Qr  . 
Lost  by  radiation  Qre. 

4.92 

0.58 

5.20 
0.58 

5.67 

0.59 

5-95 
0-59 

33°          THEKMODYNAMICS   OF   THE   STEAM-ENGINE. 

TABLE  V — Continued. 


I. 

II. 

III. 

IV. 

Intermediate  cylinder  — 
Brought  in  by  steam  .  .  Qf.  . 
During  admission.    .  .  .Qa  '  . 
During  expansion           Of,' 

131-89 
13.62 

1  8  65 

I29.6I 
11.74 

1  8  84 

137.87 
11-33 

146.64 

".75 

or    88 

During  exhaust               Qc 

O  22 

I    £7 

2  88 

During  compression  .  .  .  Q<j  '. 
Supplied  by  jacket  Qf  . 
Lost  by  radiation  Qe'  . 
Sec'd  intermediate  receiver  — 
Supplied  by  jacket  Qr'. 
Lost  by  radiation            Ore 

0.44 
6.82 

2.45 
4.20 

0.51 
7.50 
2.48 

4.04 

0.62 

7-97 
2.50 

4.27 

•41 
0.59 
8.64 
2.51 

4.22 

Low-pressure  cylinder  — 
Brought  in  by  steam  .  .  Q"  . 
During  admission  Qa" 
During  expansion  Qb" 
During  exhaust   .      .    'Oc1 

132.14 

5.85 
-9-51 

2   (^ 

130.50 
3.05 
—  7.09 

2oa 

L'*3 

I38.6I 

5-57 
-   8.65 
I   AA 

1.^4 

147-33 
5.29 
—  10.13 

During  compression.  .  .  Qdf 
Supplied  by  jacket  ....  Q/' 
Lost  by  radiation  Qe' 
Total  loss  by  radiation  — 
By  preliminary  tests,  2Qe. 
By  equation  (49)  
Power  and  economy: 
Heat-equivalents    of     works 
per  stroke  — 
-  ,       ,H.  P.  cylinder  A  IV.. 
Interm.  cylinder  AW1.. 
L    P   cylinder            AW 

••D-J 

0.00 

7.08 

4-34 

10.07 
11.68 

8.44 
7.12 

0.00 
6.  2O 
4.40 

IO.2O 
10.19 

8-34 
6-95 

0.00 
7.41 

4-45 

10.31 
8.75 

9.17 

7-77 
10  87 

0.00 

7.14 

4.47 

10.35 

8.07 

9  52 

8.42 

11.79 

Totals  

25  20 

OC     -3C 

27  8l 

Tot.  heat  furnished  by  jackets 
Distribution  of  work  — 
High-pressure  cylinder.  .  .  . 
Intermediate  cylinder  
Low-pressure  cylinder  .... 

27-58 

I.OO 

0.84 
1.14 

IO4.  Q 

27.O2 

I.OO 

0.83 

1.  21 
IO4  2 

27.71 
1.  00 

0.85 

1.19 

T  T  <J      T 

ZV   /  J 

28.45 

I.OO 

0.88 
1.24 
1  2O  3 

Steam  per  H.  P.  per  hour.  .  . 
B.  T.  U.  per  H.  P.  per  minute 

14.65 
247 

14.31 
241 

13.90 
236 

13-73 
232 

full  boiler-pressure  while  the  steam  in  the  cylinder  is  below 
atmospheric  pressure.  The  superheating  was  small  in  all 
cases — not  more  than  would  be  accounted  for  by  the  errors 
of  the  tests.  The  exhaust  waste  Qc"  from  the  low-pressure 
cylinder  in  the  triple-expansion  tests  is  very  small  in  all  cases 
— less  than  two  per  cent  of  the  heat  supplied  to  the  cylinders. 
The  apparent  absurdity  of  a  positive  value  for  Q"  in  two  of 


INFLUENCE   OF   THE   CYLINDER    WALLS.  331 

the  tests  (indicating  an  absorption  of  heat  by  the  cylinder 
walls  during  exhaust)  may  properly  be  attributed  to  the 
unavoidable  errors  of  the  test. 

In  the  fourth  test,  when  the  engine  was  developing  120.3 
horse-power,  there  were  1305  pounds  of  steam  supplied  to  the 
cylinders  in  an  hour,  and  345  pounds  to  the  steam-jackets;  so 
that  the  steam  per  horse-power  per  hour  passing  through  the 
cylinders  was 

1305  -r-  120.3  =  10.86  pounds, 
while  the  condensation  in  the  jackets  was 

345  -r-  120.3  =  2-87  pounds. 

So  that,  as  shown  on  page  245,  the  B.  T.  u.  per  horse-power 
per  minute  supplied  to  the  cylinders  by  the  entering  steam 
was  191.1,  while  the  jackets  supplied  40.6  B.  T.  U.,  making 
in  all  231.7  B.  T.  U.  per  horse-power  per  minute  for  the  heat- 
consumption  of  the  engine.  In  the  same  connection  it  was 
shown  that  the  thermal  efficiency  of  the  engine  for  this  test 
was  0.183,  while  the  efficiency  for  incomplete  expansion  in  a 
non-conducting  cylinder  corresponding  to  the  conditions  of 
the  test  was  0.222  ;  so  that  the  engine  was  running  with  0.824 
of  the  possible  efficiency.  In  light  of  this  satisfactory  con- 
clusion some  facts  with  regard  to  the  test  are  interesting. 

It  will  be  noted  that  149.84  B.  T.  U.  per  stroke  are  brought 
in  by  the  steam  supplied  to  the  high-pressure  cylinder  and 
that  28.45  B-  T-  u-  Per  stroke  are  supplied  by  the  steam- 
jackets;  and  that,  further,  29.73  B.  T.  u.  are  changed  into  work 
while  10.35  are  radiated.  Thus  it  appears  that  the  jackets 
furnished  almost  as  much  heat  as  was  required  to  do  all  the  work 
developed.  Of  the  heat  furnished  by  the  jackets  something 
more  than  a  third  was,  radiated ;  the  other  two-thirds  may 
fairly  be  considered  to  have  been  changed  into  work,  since 
the  exhaust  waste  of  the  low-pressure  cylinder  was  practically 
zero. 

Table  VI   gives  the   results  of  tests  made  on  a  vertical 


332  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

TABLE   VI. 

TRIPLE-EXPANSION    VERTICAL   PUMPING-ENGINE   AT 
MILWAUKEE,  WISCONSIN. 

CYLINDER    DIAMETERS,    28,    48,    AND    74    INCHES;    STROKE,    60    INCHES. 

By  Professor  R.  C.  CARPENTER,  7^rans.  Am.  Soc.  Mech.  Engrs., 
vol.  xv,  p.  313. 

Duration,  hours 24 

Revolutions  per  minute 20.3 

Pressures,  pounds  per  square  inch  : 

Gauge  at  throttle 121.5 

Vacuum 13.8 

Barometric 14.5 

High-pressure  jackets 121.4 

Intermediate  and  low-pressure  jackets 56.5 

First  receiver 32.4 

Second  receiver 13.8 

Moisture  in  steam,  per  cent i.i 

Steam  used  in  jackets,  per  cent. 9.3 

Indicated  horse-power 573-9 

Pump,  horse-power 521.0 

Friction,  per  cent g.2 

Steam  per  horse-power  per  hour n.8 

B.  T.  U.  per  horse-power  per  minute 217.6 

Hirn's    analysis,    interchanges    of    heat   between    the    walls    of    the 
cylinder  and  the  steam  ;   in  per  cent  of  total  heat  per  stroke  : 
High-pressure  cylinder — 

Absorbed  during  admission 10.5 

Restored  during  expansion —  7.9 

Rejected  during  exhaust „ —  4.7 

Absorbed  during  compression 0.2 

Intermediate  cylinder — 

Absorbed  during  admission n.8 

Restored  during  expansion —6.2 

Rejected  during  exhaust —7-2 

Given  up  during  compression —  0.2 

Low-pressure  cylinder — 

Absorbed  during  admission 2.1 

Restored  during  expansion —  o.  i 

Rejected  during  exhaust —  21.2 

Given  up  during  compression —  1.2 

Thermodynamic  efficiency 0.194 


INFLUENCE   OF   THE   CYLINDER    WALLS.  333 

triple-expansion  pumping-engine,  together  with  an  application 
of  Hirn's  analysis,  which  is  especially  interesting  as  the  engine 
was  made  by  the  builders  of  the  experimental  engines  at  the 
Massachusetts  Institute  of  Technology,  and  it  ran  under 
much  the  same  conditions.  Its  higher  efficiency  and  better 
economy  was  due  in  part  to  the  fact  that  the  engine  was 
larger  and  superior  in  certain  details,  but  more  particularly  to 
the  good  vacuum  attained.  The  principal  difference  in  the 
results  of  the  application  of  Hirn's  analysis  to  the  tests  on  the 
two  engines  is  in  the  heat  rejected  by  the  walls  during 
exhaust;  for  the  experimental  engine  these  quantities  are 
small  for  all  three  cylinders,  and  in  particular  is  practically 
zero  for  the  low-pressure  cylinder,  while  for  the  pumping- 
engine  they  are  of  considerable  magnitude,  and  the  exhaust 
waste  for  the  low-pressure  cylinder  is  large.  So  far  as  any 
significance  can  be  attached  to  this  comparison  it  shows  that 
a  considerable  exhaust  waste  is  not  incompatible  with  a  high 
economy. 

Alternate  Method  for  Compound  Engines. — When  the 
method  of  applying  Hirn's  analysis  to  a  compound  engine, 
which  has  just  been  explained  and  exemplified,  can  be  used 
it  is  most  satisfactory,  as  the  comparison  of  the  observed  and 
calculated  radiation  losses  gives  an  excellent  check  on  the 
accuracy  of  the  test  in  general.  If,  however,  it  should  be 
impossible  in  any  case  to  properly  account  for  the  heat  added 
to  or  lost  by  the  steam  in  the  intermediate  receiver,  we  may 
still  make  an  application  of  Hirn's  analysis  by  the  following 
method. 

There  is  no  difficulty  in  making  the  application  to  the 
high-pressure  cylinder  by  the  method  already  explained. 
The  trouble  comes  in  the  determination  of  the  heat  Q  sup- 
plied by  the  steam  which  enters  the  low-pressure  cylinder. 
But  by  applying  equation  (292)  to  the  low-pressure  cylinder 
we  have 

-  Wt-  Wd\     (297) 


334  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and  consequently 
&  =  &-Qj'+ArK+G(i,,-q,)+A(Wa+Wt-  W.-  Wd\  (298) 

by  aid  of  which  equation  Q  may  be  eliminated  from  the  equa- 
tion for  (2«/,  the  heat  absorbed  by  the  wall  of  the  low-pressure 
cylinder  during  admission.  Therefore  we  have  for  the  equa- 
tions for  a  compound  engine 

G«  =  Q  +  7.  -A-  AWa;    .     .     .     ••'.>;  (299) 

g,  =  /1-/1-^Pn;    .     .....     .     .     .  (300) 

c);.  (301) 

-,  (302) 


G.'  -  G/  -  QJ  +  MK  +  G(qk  -  ?,)  +  /.  -/, 

-  Wc-  W4)i    .    .     .     (303) 


G*'  -  //  -  //  -  A  m'-,   .  .  .  .  <  .  /  *  (304) 

Q^It-i:  -Mq,-G(qk-q^  +  AW;-     .     (305) 

e/-/3/-A/  +  ^^.     -    •  '.-..•••;;  '-.-..•;  .    (306) 

Maire's  Tests.  —  In  Table  VII  is  given  a  large  number 
of  tests  on  important  engines  of  various  types,  together  with 
the  application  of  Hirn's  analysis.  Some  of  the  engines 
tested,  such  as  the  Cornish  engine  and  the  Bull  engine,  are 
out  of  date,  and  the  interest  in  some  others  is  impaired  by 
the  low  pressure  of  steam  in  the  boiler.  It  is  also  unfor- 
tunate that  Maire  did  not  separate  the  interchanges  of  heat 
during  the  admission  and  expansion  in  the  low-pressure 
cylinder,  nor  does  his  report  allow  us  to  make  the  separation. 
We  have  consequently  for  the  low-pressure  cylinder  only  the 
exhaust  waste  Qe  and  the  exchange  Qd  for  compression. 
Nevertheless  the  table  is  instructive  and  important. 


INFLUENCE   OF   THE    CYLINDER    WALLS.  335 

The  dimensions  of  the  engines  and  the  conditions  of  the 
tests  were  as  follows: 

The  steam-consumption  was  determined  by  measuring  the 
feed-water  supplied  to  the  boiler.  The  steam  condensed  in 
the  steam-jackets  was  collected  and  weighed  separately.  The 
air-pump  discharge  was  allowed  to  flow  through  an  orifice 
under  a  measured  head ;  the  coefficient  of  discharge  for  the 
orifice  was  determined  by  direct  experiments.  The  per  cent 
•of  priming  in  the  steam  was  determined  by  calorimetric  tests. 

The  test  I  was  made  on  a  single-cylinder  rotative  pump- 
ing-engine,  having  a  diameter  of  45  inches  and  a  stroke  of 
5  feet  6  inches.  The  sides  and  ends  of  the  cylinder  were 
jacketed  with  boiler  steam.  The  steam  was  distributed  by 
separate  slide-valves  near  the  ends  of  the  cylinder,  with 
expansion-plates  adjustable  by  hand,  on  the  backs  of  the 
main  valves. 

The  tests  2,  3,  and  4  were  made  on  a  Woolf  beam-engine 
driving  a  flour-mill.  The  cylinders  were  24^  inches  in 
diameter  by  3  feet  5  inches  stroke,  and  38  inches  diameter 
by  5  feet  6  inches  stroke,  and  were  steam-jacketed  on  the 
sides  only.  The  steam  was  distributed  to  the  high-pressure 
cylinder  by  a  slide-valve  with  cut-off  plates  on  the  back,  and 
to  the  low-pressure  cylinder  by  a  piston-valve,  all  being 
worked  by  eccentrics. 

The  tests  5  and  6  were  made  on  an  unjacketed  horizontal 
Woolf  engine,  of  a  type  very  commonly  used  in  factories  in 
Lancashire.  The  cylinders  were  i$f  and  28^  inches  in 
diameter  by  4  feet  3  inches  stroke.  The  piston  speed  was 
about  680  feet  per  minute  and  the  load  was  light,  so  that  the 
steam  was  much  wire-drawn. 

The  test  7  was  made  on  a  compound  beam  receiver-engine 
with  the  cranks  at  right  angles,  working  pumps  directly  from 
the  beams.  The  cylinders  were  2 1  and  36  inches  in  diameter, 
and  the  stroke  was  5  feet  6  inches.  Both  cylinders,  with  the 
exception  of  the  high-pressure  cylinder  and  the  receiver- 
covers,  were  jacketed  with  boiler  steam.  The  steam  was 


336 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


TABLE  VII. 

APPLICATION  OF  HIRN'S  ANALYSIS  TO  SIMPLE  AND  COMPOUND  ENGINES. 
By  GEORGE  MAIRE. 
Proc.  of  the  Inst.  of  Civ.  Engrs.,  vols.  LXX  and  LXXIX. 

•XDU3IDUJ3 

IBDijsjoaq}  umtnixBj^ 

d 

ISS 

odd 

6  d 

0 

d 

d  d 

d  d 

rn 

O 

d  d 

SFS 

odd 

•uim  jad  'j3Mod 
-asjoq  jsd  'fl   i  'g 

f>  fO 

i 

i 

00 

H 

H 

* 

« 

H» 

•spunod  'anoq 
jad  'd  -q  jad  OJBSIS 

i? 

00  00    O 

s; 

10 

ff 

N  VO 

S  «" 

s> 

^2^- 

SO   JO  10 

Percentage  of  water  in 
cylinder. 

jo  pua  ?v 

«a 

11 

o 

:  ; 

5? 

^Jr2 

•japuijAo 
•d  -q  '3Jf6j}s 
jo  pus  jv 

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T»-    M    00 

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to  •* 

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'43Mod-3SJOH 

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10  •* 

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10 

00    O  N 

§ 

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mli.p. 

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INFLUENCE   OF   THE    CYLINDER    WALLS.  337 


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Single-cylinder  beam! 
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33$  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

distributed  by  slides,  one  at  each  end  of  each  of  the  cylinders, 
with  cut-off  plates  adjustable  by  hand. 

The  test  8  was  made  on  a  Cornish  engine  working  a 
single-acting  piston-pump  direct  from  the  beam,  and  having 
the  usual  Cornish,  double-beat,  steam,  equilibrium,  and 
exhaust-valves,  a  single-acting  air-pump,  and  a  jet-condenser; 
the  cylinder  was  68J  inches  in  diameter  by  8  feet  stroke,  and 
was  jacketed  on  the  sides  with  boiler  steam.  The  pump 
delivered  its  water  on  the  up  or  steam  stroke,  so  that  the 
preponderance  of  weight  on  the  pump-pole  was  only  enough 
to  overcome  the  suction  lift.  The  valves  and  piston  were 
inspected  to  assure  their  tightness  before  the  test.  The 
engine  was  doing  the  highest  duty  at  the  West  Middlesex 
Waterworks,  and  was  taken  as  one  of  the  best  engines  of  its 
type  now  working.  This  type  of  engine  was  developed  in 
Cornwall,  where  it  was  used  to  pump  water  from  deep  mines 
by  a  pump-rod  hung  directly  from  one  end  of  the  beam  while 
the  piston  was  hung  from  the  other  end  of  the  beam.  It  had 
no  fly-wheel,  but  the  pump-rod,  beam,  and  counter-weights 
made  in  the  aggregate  a  large  reciprocating  mass,  that 
absorbed  work  during  the  first  part  of  the  stroke  when  the 
steam-pressure  in  the  cylinder  was  high,  and  restored  that 
work  and  assisted  the  steam  to  complete  the  stroke,  after  it 
had  lost  pressure  through  expansion,  during  the  latter  part  of 
the  stroke.  Such  a  reciprocating  mass  is  essential  to  the 
proper  action  of  the  engine  with  expansion.  The  pumps  of 
the  original  engines  were  worked  by  the  weight  of  the  rods 
during  the  return  or  equilibrium  stroke,  at  which  time  there 
was  free  communication  between  the  two  ends  of  the  cylinder. 
The  lower  end  of  the  cylinder  was  open  to  the  condenser 
during  the  steam-stroke. 

The  tests  9  and  10  were  made  on  a  single-cylinder  beam 
rotative  pumping-engine,  having  a  diameter  of  32  inches  and 
a  stroke  of  5  feet  6  inches.  The  cylinder  sides  and  base  were 
jacketed  with  boiler  steam.  Steam  was  distributed  by  slide- 


INFLUENCE   OF   THE   CYLINDER    WALLS.  339 

valves  at  the  top  and  bottom  of  the  cylinder,  with  cut-off 
plates,  adjustable  by  hand,  on  the  backs  of  the  main  valves. 

The  tests  n  and  12  were  made  on  a  single-cylinder  beam 
rotative  engine,  similar  to  the  one  just  described,  and  taking 
steam  from  the  same  boilers.  The  cylinder  was  27  inches  in 
diameter  by  6  feet  stroke. 

The  test  13  was  made  on  a  Bull  engine  with  a  cylinder  68 
inches  in  diameter  by  10  feet  stroke,  driving  direct  a  45-inch 
plunger-pump,  and  forcing  water  to  a  height  of  40  to  55  feet. 
The  valves  and  gear  were  of  the  usual  Cornish  pattern,  and 
the  sides  and  base  of  the  cylinder  were  steam-jacketed.  This 
type  of  engine  differs  from  the  Cornish  engine  in  not  having 
a  beam,  and  though  the  pump-rod  is  loaded  there  is  seldom 
sufficient  reciprocating  mass  to  allow  of  much  expansion.  In 
the  case  of  the  engine  tested  only  if  expansions  could  be 
obtained.  For  convenience,  the  steam-stroke  is  detailed 
under  the  heading  of  the  high-pressure  cylinder,  and  the 
exhaust-stroke  under  the  heading  of  the  low-pressure  cylinder. 

The  tests  14  and  15  were  made  on  a  Woolf  beam  rotative 
engine,  working  a  double-acting  pump.  The  cylinders  were 
29  inches  diameter  by  5  feet  5  inches  stroke,  and  47^  inches 
diameter  by  8  feet  stroke,  and  jacketed  with  steam  on  the 
sides  and  ends. 

The  most  interesting  tests  for  our  present  purpose  are 
2,  3,  and  4,  since  they  show  how  a  compound  engine  is 
affected  by  steam-jackets.  It  appears  that  in  this  case  the 
interchanges  of  heat  for  the  high-pressure  cylinder  are  not 
much  affected,  though  there  is  some  increase  in  the  heat 
restored  during  expansion,  and  the  exhaust  waste  is  less  when 
steam  is  used  in  the  jackets.  But  the  exhaust  waste  for  the 
low-pressure  cylinder  is  very  much  reduced,  and  may  in  a  large 
measure  account  for  the  gain  in  economy. 

The  comparison  of  test  7  with  tests  14  and  15  is  instruc- 
tive, for  the  latter  show  practically  no  exhaust  waste  from  the 
low-pressure  cylinder,  while  the  former  has  a  considerable 
exhaust  waste ;  nevertheless  the  economy  for  test  7  is  notably 


34°  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

better  than  for  tests  14  and  15.  The  advantage  is  probably 
due  to  the  higher  steam-pressure  and  larger  number  of 
expansions  enjoyed  by  the  engine  represented  by  test  7. 
This  is  only  one  more  example  to  show  that  while  the  exhaust 
waste  is  always  a  direct  loss  it  may  be  unadvisable  to  try  to 
reduce  it  to  zero  by  the  lavish  application  of  steam-jackets  or 
by  other  ways  of  supplying  heat  to  steam  on  its  way  through 
a  compound  or  multiple-expansion  engine.  It  will  be  shown 
later  that  it  is  possible  to  overdo  the  application  of  heat  in 
this  way  and  so  injure  the  economy  of  the  engine;  the  best 
result  appears  to  be  attained  by  a  judicious  or  a  fortunate 
compromise  of  the  gain  from  expansion  and  the  loss  from 
condensation  and  evaporation,  together  with  the  amelioration 
of  the  latter  by  the  use  of  steam-jackets  and  intermediate 
reheaters. 

Quality  of  Steam  at  Compression. — In  all  the  work  of 
this  chapter  the  steam  in  the  cylinder  at  compression  has  been 
considered  to  be  dry  and  saturated,  and  it  has  been  asserted 
that  little  if  any  error  can  arise  from  this  assumption.  It  is 
clear  that  some  justification  for  such  an  assumption  is  needed, 
for  a  relatively  large  weight  of  water  in  the  cylinder  would 
occupy  a  small  volume  and  might  well  be  found  adhering  to 
the  cylinder  walls  in  the  form  of  a  film  or  in  drops;  such  a 
weight  of  water  would  entirely  change  our  calculations  of  the 
interchanges  of  heat.  The  only  valid  objection  to  Hirn's 
analysis  is  directed  against  the  assumption  of  dry  steam  at 
release.  Indeed,  when  the  analysis  was  first  presented  some 
critics  asserted  that  the  assumption  of  a  proper  amount  of 
water  in  the  cylinder  is  all  that  is  required  to  reduce  the  cal- 
culated interchanges  of  heat  to  zero.  It  is  not  difficult  to 
refute  such  an  assertion  from  almost  any  set  of  analyses,  but 
unfortunately  such  a  refutation  cannot  be  made  to  show  con- 
clusively that  there  is  little  or  no  water  in  the  cylinder  at 
compression ;  in  every  case  it  will  show  only  that  there  must 
be  a  considerable  interchange  of  heat. 

For  the  several  tests  on  the  Hirn  engine  given  in  Table 


INFLUENCE   OF   THE   CYLINDER    W 'ALLS.  34! 

Ill,  Hallauer  determined  the  amount  of  moisture  in  the  steam 
in  the  exhaust-pipe,  and  found  it  to  vary  from  3  to  10  per 
cent.  Professor  Carpenter*  says  that  the  steam  exhausted 
from  the  high-pressure  cylinder  of  a  compound  engine  showed 
12  to  14  per  cent  of  moisture.  Numerous  tests  made  in  the 
laboratory  of  the  Massachusetts  Institute  of  Technology  show 
there  is  never  a  large  percentage  of  water  in  exhaust-steam. 
Finally,  such  a  conclusion  is  evident  from  ordinary  observation. 
Starting  from  this  fact  and  assuming  that  the  steam  in  the 
cylinder  at  release  is  at  least  as  dry  as  the  steam  in  the 
exhaust-pipe,  we  are  easily  led  to  the  conclusion  that  our 
assumption  of  dry  steam  is  proper.  Professor  Carpenter 
reports  also  that  a  calorimeter  test  of  steam  drawn  from  the 
cylinder  during  compression  showed  little  or  no  moisture. 
Nevertheless  there  would  still  remain  some  doubt  whether  the 
assumption  of  dry  steam  at  compression  is  really  justified, 
were  we  not  so  fortunate  as  to  have  direct  experimental 
knowledge  of  the  fluctuations  of  temperature  in  the  cylinder 
walls. 

Dr.  Hall's  Investigations. — For  the  purpose  of  studying 
the  temperatures  of  the  cylinder- walls  Dr.  E.  H.  Hall  used 
a  thermo-electric  couple,  represented  by  Fig.  74.  /  is  a  cast- 


FIG.  74. 

iron  plug  about  three-quarters  of  an  inch  in  diameter,  which 
could  be  screwed  into  the  hole  provided  for  attaching  an 
indicator-cock  to  the  cylinder  of  a  steam-engine.  The 
inner  end  of  the  plug  carried  a  thin  cast-iron  disk,  which  was 
assumed  to  act  as  a  part  of  the  cylinder- wall  when  the  plug 
was  in  place.  To  study  the  temperature  of  the  outside  sur- 
face of  the  disk  a  nickel  rod  ^V  was  soldered  to  it,  making  a 

*  Trans.  Am.  Soc.  Mech.  Engrs.,  vol.  XII,  p.  811. 


342  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

thermo-electric  couple.  Wires  from  /  and  N  led  to  another 
couple  made  by  soldering  together  cast-iron  and  nickel,  and 
this  second  couple  was  placed  in  a  bath  of  paraffine  which 
could  be  maintained  at  any  desired  temperature.  In  the 
electric  circuit  formed  by  the  wires  joining  the  two  thermo- 
electric couples  there  was  placed  a  galvanometer  and  a  circuit- 
breaker.  The  circuit-breaker  was  closed  by  a  cam  on  the 
crank-shaft,  which  could  be  set  to  act  at  any  point  of  the 
revolution.  If  the  temperature  of  the  outside  of  the  disk  S 
differed  from  the  temperature  of  the  paraffine  bath  at  the 
instant  when  contact  was  made  by  the  cam,  a  current  passed 
through  the  wires  and  was  indicated  by  the  galvanometer. 
By  properly  regulating  the  temperature  of  the  bath,  the 
current  could  be  reduced  and  made  to  cease,  and  then  a 
thermometer  in  the  bath  gave  the  temperature  at  the  surface 
of  the  disk  for  the  instant  when  the  cam  closed  the  electric 
circuit.  Two  points  in  the  steam-cycle  were  chosen  for 
investigation,  one  immediately  after  cut-off  and  the  other 
immediately  after  compression,  since  they  gave  the  means  of 
investigating  the  heat  absorbed  during  compression  and 
admission  of  steam,  and  the  heat  given  up  during  expansion 
and  exhaust. 

Three  different  disks  were  used:  the  first  one  half  a  milli- 
metre thick,  the  second  one  millimetre  thick,  and  a  third 
two  millimetres  thick.  From  the  fluctuations  of  temperature 
at  these  distances  from  the  inside  surface  of  the  wall  some 
idea  could  be  obtained  concerning  the  variations  of  tempera- 
ture at  the  inner  surface  of  the  cylinder,  and  also  how  far  the 
heating  and  cooling  of  the  walls  extended. 

The  account  given  here  is  intended  only  to  show  the 
general  idea  of  the  method,  and  does  not  adequately  indicate 
the  labor  and  difficulties  of  the  investigation  which  involved 
many  secondary  investigations,  such  as  the  determination  of 
the  conductivity  of  nickel.  Having  shown  conclusively  that 
there  is  an  energetic  action  of  the  walls  of  the  cylinder, 
Dr.  Hall  was  unable  to  continue  his  investigations. 


INFLUENCE   OF   THE   CYLINDER    WALLS.  343 

Callendar  and  Nicolson's  Investigations. — A  very  re- 
fined and  complete  investigation  of  the  temperature  of  the 
cylinder  walls  and  also  of  the  steam  in  the  cylinder  was  made 
by  Messrs.  Callendar  and  Nicholson*  in  1895  at  the  McGill 
University,  by  the  thermoelectric  method. 

The  wall  temperatures  were  determined  by  a  thermoelec- 
tric couple  of  which  the  cylinder  itself  was  one  element  and 
a  wrought-iron  wire  was  the  other  element.  To  make  such  a 
couple,  the  cylinder-wall  was  drilled  nearly  through,  and  the 
wire  was  soldered  to  the  bottom  of  the  hole.  Eight  such 
couples  were  established  in  the  cylinder-head,  the  thickness 
of  the  unbroken  wall  varying  from  o.oi  of  an  inch  to  0.64  of 
an  inch.  Four  pairs  of  couples  were  established  along  the 
cylinder-barrel,  one  near  the  head,  and  the  others  at  4  inches, 
6  inches,  and  12  inches  from  the  head.  One  of  each  pair  of 
wall  couples  was  bored  to  within  0.04  of  an  inch,  and  the 
other  to  0.5  of  an  inch  of  the  inside  surface  of  the  cylinder. 
Other  couples  were  established  along  the  side  of  the  cylinder 
to  study  the  flow  of  heat  from  the  head  toward  the  crank  end. 

The  engine  used  for  the  investigations  was  a  high-speed 
engine,  with  a  balanced  slide-valve  controlled  by  a  fly-wheel 
governor.  During  the  investigations  the  cut-off  was  set  at  a 
fixed  point  and  the  speed  was  controlled  externally.  By  the 
addition  of  a  sufficient  amount  of  lap  to  prevent  the  valve 
from  taking  steam  at  the  crank  end  the  engine  was  made 
single-acting.  The  normal  speed  of  the  engine  was  250  revo- 
lutions per  minute,  but  during  the  investigations  the  speed 
was  from  40  to  90  revolutions  per  minute.  The  diameter  of 
the  cylinder  was  10.5  inches  and  the  stroke  of  the  piston  was- 
12  inches.  The  clearance  was  ten  per  cent  of  the  piston  dis- 
placement. 

The  indicator-diagram  for  a  cut-off  at  one-fifth  stroke,  at 
which  most  of  the  investigations  were  made,  is  given  by 
Fig.  75.  From  the  indicated  pressure  the  temperatures  of 

*  Proceedings  of  the  Inst.  Civ.  Engrs.,  vol.  CXXXH. 


344  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

the  steam  at  various  piston  positions  could  be  readily  deter- 
mined by  aid  of  a  table  of  the  properties  of  saturated  steam. 


FIG.  75- 


400' 


300* 


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FIG.  76. 

In  Fig.  76  the  indicated  steam  temperatures  determined  from 
Fig.  75  are  plotted  as  ordinates,  with  sixtieths  of  a  revolution 


INFLUENCE   OF   THE    CYLINDER    WALLS.  345 

for  abscissae.  The  zero  of  abscissae  is  at  the  beginning  of  the 
forward  stroke  and  the  rise  of  temperature  corresponds  with 
the  admission  of  steam  shown  on  Fig.  75.  The  temperature 
of  course  remains  constant  for  the  part  of  the  revolution  which 
corresponds  to  the  steam  line  of  the  indicator.  There  is  then 
a  gradual  fall  of  temperature  corresponding  to  the  expansion, 
and  a  rapid  drop  corresponding  to  release.  After  release  the 
back-pressure  temperature  is  constant  till  the  beginning  of 
compression,  and  during  compression  there  is  a  rapid  rise  of 
temperature  corresponding  to  the  increase  of  pressure.  The 
diagram  Fig.  73  begins  at  ||-  of  the  revolution  in  order  that 
the  most  interesting  events  shall  be  recorded  in  the  middle  of 
the  diagram.  The  crosses  in  the  diagram  show  the  tempera- 
ture of  the  steam  as  determined  by  the  platinum  thermometer 
in  the  piston  of  the  engine.  The  divergency  between  the 
crosses  and  the  full  line  representing  indicated  temperatures 
is  considered  by  the  investigators  to  be  larger  than  the  com- 
bined errors  of  the  indicator  and  platinum  thermometer. 
But  at  atmospheric  pressure  there  are  three  degrees  increase 
of  temperature  for  each  pound  increase  of  pressure,  and  even 
at  70  pounds  pressure  there  is  one  degree  for  a  pound  increase 
of  pressure.  Taking  into  consideration  also  the  fact  that  the 
discrepancy  is  always  on  the  side  where  the  friction  and  lag 
of  the  indicator  tend  to  place  it,  the  discrepancy  does  not 
appear  to  require  further  explanation,  unless  it  may  be  for 
the  steam  line;  it  is  of  course  possible  that  there  may  be 
superheated  steam  in  the  middle  of  the  cylinder  during  the 
admission  of  steam,  together  with  a  film  of  water  on  the  cooler 
walls  of  the  cylinder. 

The  mean  temperature  of  the  cylinder-head  is  represented 
by  a  dotted  line  just  above  300°  F.  The  mean  temperature 
of  the  steam  is  shown  by  a  full  line  at  247°  F.  The  dotted 
line  lettered  Metal  cycle  will  be  explained  later. 

Fig.  77  gives  a  similar  diagram  of  indicated  steam  tempera- 
tures for  another  test,  together  with  a  diagram  of  temperatures 
by  a  platinum  thermometer  near  the  surface  of  the  cylinder 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


head.  During  all  of  the  exhaust  the  steam  near  the  cylinder 
head  is  strongly  superheated,  and  compression  carries  the 
superheating  far  beyond  the  temperature  of  saturated  steam 
during  the  admission.  As  steam  comes  into  the  cylinder  the 
temperature  near  the  cylinder-head  falls  rapidly  till  it  passes 
below  that  of  saturated  steam  just  before  cut-off.  Though 
the  temperature  shown  by  the  platinum  thermometer  con- 
tinues to  fall  after  cut-off  it  soon  rises  beyond  that  shown  by 


200° 


\v 


350° 


250° 


1550550  5101520253035404550 

Time  in  sixtieths  of  a  revolution  from  back  end  of  stroke 

FIG.  77. 

the  indicator.  T,his  is  considered  by  the  investigators  to 
show  that  the  evaporation  from  the  cylinder-head  is  probably 
complete  soon  after  cut-off.  Certainly  the  superheating  dur- 
ing compression  disposes  of  any  assumption  that  there  is  any 
considerable  amount  of  water  in  the  cylinder  at  the  beginning 
of  compression. 

Fig-  78  gives  a  similar  diagram  of  indicated  steam  tem- 
peratures, and  also  a  diagram,  represented  by  the  dotted  curve, 
of  the  changes  of  temperature  near  the  inner  surface  of  the 
cylinder.  The  scale  for  the  full  line  representing  indicated 
pressures  is  given  at  the  left,  the  scale  for  the  changes  of  the 
temperature  of  the  wall  is  given  at  the  right.  The  ther- 
moelectric couple  by  which  the  wall  temperatures  were  deter- 


INFLUENCE   OF  THE   CYLINDER    WALLS. 


347 


mined  was  in  the  cylinder-head,  and  had  a  thickness  of  o.oi 
of  an  inch  of  unperforated  wall  between  it  and  the  inner 
surface. 

A  comparison  of  the  temperatures  of  the  cylinder-head 
and  of  the  side  wall  near  the  head  is  very  instructive.  In 
the  first  place  the  mean  temperature  of  the  side  was  14°.  3 
lower  than  that  of  the  wall ;  and  secondly,  the  temperature 
of  the  side  varied  more.  Thus  the  range  of  variation  for  the 
head  was  4°. 9,  while  that  for  the  side  near  the  head  was 
1 3°.  5.  The  general  character  of  the  cycle  of  temperature 


400° 


350° 


300° 


250° 


/ 


alR<?mp 


Y*. 


297° 


-•j 

•8 
»°1 


4550550  5101520253035404550 

Time  in  sixtieths  of  a  revolution  from  back  end  of  stroke 

FIG.  78. 

changes  for  the  side  was  similar  to  that  for  the  head.  The 
mean  temperature  of  the  cylinder-wall  decreased  from  the 
head  toward  the  crank  end,  as  might  be  expected  for  a  single- 
acting  engine;  and  there  was  a  considerable  flow  of  heat  in 
the  same  direction.  A  double-acting  engine  cylinder  would 
differ  in  this  respect,  as  the  flow  of  heat  would  be  from  both 
ends  to  the  middle,  provided  there  were  any  perceptible  flow. 
The  temperature  cycles  for  different  points  along  the  side  of 
the  cylinder  were  in  general  like  the  cycle  for  the  end  near 
the  head:  the  greatest  difference  for  a  point  beyond  cut-off 
being  due  to  its  sudden  exposure  to  steam  when  it  was  un- 


THERMODYNAMICS    OF   THE   STEAM-ENGINE. 


covered  by  the  piston.  Of  course  some  difference  in  the 
cycle  was  produced  by  the  fall  of  the  mean  wall  temperature 
from  the  head  toward  the  crank. 

The  eight  thermo-electric  couples  in  the  head,  with  thick- 
nesses of  unbroken  wall  varying  from  o.oi  of  an  inch  to  0.64 
of  an  inch  afforded  means  of  determining  the  law  of  the  flow 
of  heat  to  and  from  the  cylinder-wall.  These  and  the  pairs 
of  couples  along  the  side  of  the  cylinder  gave  the  means  of 
calculating  the  heat  absorbed  by  and  restored  by  the  cylinder. 
The  methods  of  reducing  the  observations  and  making  calcu- 
lations are  too  intricate  to  be  given  here;  it  will  suffice  to 
give  some  of  the  results. 

The  following  table  gives  the  areas,  temperatures,  and  the 
heat  absorbed  during  a  given  test  by  the  various  surfaces 
exposed  to  steam  at  the  end  of  the  stroke,  i.e.,  the  clearance 
surface. 

TABLE  VIII. 

CYCLICAL    HEAT-ABSORPTION    FOR    CLEARANCE   SURFACES. 


Portions  of  surface  considered. 

Area 
of  surface, 
square  feet. 

Mean 
temperature, 

Heat  absorbed 
B.  T.  U. 
per  minute. 

Cover  face,  10.5  inches  diameter  .  .  . 
Cover  side    3.0  inches      

0.60 
O   7O 

305 

'IQC 

68 

7Q 

Piston  face,  10.5  inches  diameter  .  . 
Piston  side    o  5  inch                       .... 

0.60 
on 

2Q5 
OQC 

no 

2O 

Barrel  side    3  o  inches                 

O  71 

2Q7 

TO-l 

O  1  2 

2QI 

28 

Ports  and  valves            .           ...... 

O  QO 

•2QC 

IO2 

37J. 

jui 

DJU 

The  heat  absorbed  by  the  side  of  the  cylinder-wall  uncov- 
ered by  the  piston  up  to  0.25  of  the  stroke  was  estimated  to 
be  55  B.  T.  U.  per  minute,  which  added  to  the  above  sum 
gives  585  B.  T.  U. ;  from  which  it  appears  that  90  per  cent  of 
the  condensation  is  chargeable  to  the  clearance  surfaces. 
Further  inspection  shows  that  the  condensation  on  the  piston 
and  the  barrel  is  much  more  energetic  than  on  the  cover  or 


INFLUENCE   OF   THE   CYLINDER    WALLS. 


349 


head.  For  example,  the  face  of  the  piston  absorbs  1 10 
B.  T.  U.  while  the  face  of  the  cover  absorbs  only  68  B.  T.  U. ; 
and  the  side  of  the  cover  and  of  the  barrel,  each  3  inches  long, 
absorb  79  and  123  B.  T.  U.,  respectively.  This  relatively 
small  action  of  the  surfaces  of  the  head  indicates  that  less 
gain  is  to  be  anticipated  from  the  application  of  a  steam- 
jacket  to  the  head  than  to  the  barrel  of  a  steam-engine ;  tests 
on  engines  confirm  this  conclusion. 

The  exposed  surfaces  at  the  side  of  the  cylinder-head  and 
the  corresponding  side  of  the  barrel  are  due  to  the  use  of  a 
deeply  cored  head  which  protrudes  three  inches  into  the 
counterbore  of  the  cylinder,  and  which  has  the  steam-tight 
joint  at  the  flange  of  the  head.  It  would  appear  from  this 
that  a  notable  reduction  of  condensation  could  be  obtained 
by  the  simple  expedient  of  making  a  thin  cylinder- head. 

The  final  results  of  the  investigations  and  the  comparison 
of  the  condensation  due  to  the  heat  absorbed  by  the  walls  of 
the  cylinder  are  given  in  Table  IX.  Considering  the  intricacy 
and  difficulty  of  the  investigations  the  comparison  of  indicated 
and  calculated  condensations  and  evaporations  must  be  con- 

TABLE   IX. 

INFLUENCE   OF   THE  WALLS   OF   THE   CYLINDER. 
CALLENDAR  AND  NICHOLSON,  Proc.  Inst.  Civ.  Engrs.,  1897. 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

Duration,  minutes  
Revolutions  per  minute  . 

«r« 

68 
45-7 

55 
47.7 

79 
70.4 

76 

73-4 

8?57 

25 

87  Q 

89  2 

94  '4 

98.1 

Gross  steam  per  revolution  
Leakage  correction  

0.1422 

0.1437 

0.1483 
0.0990 

0.1094 

0.1036 

o.  1000 

0.0856 

Net  steam  per  revolution  

0.0418 

0.0461 

0.0493 

0.0397 

0.0409 

0.0424 

Steam  caught  at  compression  
Weight  of  mixture  in  cylinder  .  .  . 
Indicated  steam  at  quarter  stroke. 
Indicated  steam  at  release  .... 

0.0107 
0.0525 

o  .  0407 

0.0104 
0.0565 
0.0414 

0.0103 
0.0596 
0.0437 
0.0488 

0.0099 
0.0496 
0.0418 

0.0090 
0.0507 
0.0394 

O.OIOO 

0.0524 
0.0408 

0.0105 
0.0467 
0.0393 

Increase  of  indicated  weight  
Adiabatic  condensation  
Indicated  evaporation  .... 

0.0059 
0.0019 

0.0042 

O.OO2O 

0.0051 

O.OO2I 

0.0042 

O.OO2O 

0.0042 
0.0019 

0.0046 

O.OO2O 

0.0033 

O.OOIQ 

indicated  condensation  
Calculated  condensation  
Indicated  horse-power  
Steam  per  H.P.  per  hour,  pounds. 

0.0118 
0.0148 
4.10 
26.8 

O.OI5I 
0.0142 

4-34 
29.1 

0.0159 
0.0136 

4.78 
39-5 

0.0078 
0.0092 
7-02 
23-8 

0.0113 
0.0089 
6.67 
27.1 

0.0116 
0.0080 

7.71 
26.9 

0.0074 
0.0067 

8.81 

23.8 

35°  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

ceded  to  be  very  satisfactory,  and  it  must  be  admitted  that 
the  interchanges  of  heat  are  mainly,  if  not  entirely,  due  to  the 
metal  of  the  cylinder-wall  and  not  to  water  which  remains  in 
the  cylinder  from  one  stroke  to  the  next. 

Leakage  of  Valves. — Preliminary  tests  when  the  engine 
was  at  rest  showed  that  the  valve  and  piston  were  tight. 
The  valve  was  further  tested  by  running  it  by  an  electric 
motor  when  the  piston  was  blocked,  the  stroke  of  the  valve 
being  regulated  so  that  it  did  not  quite  open  the  port,  where- 
upon it  appeared  that  there  was  a  perceptible  but  not  an  im- 
portant leak  past  the  valve  into  the  cylinder.  There  was  also 
found  to  be  a  small  leakage  past  the  piston  from  the  head  to 
the  crank  end. 

But  the  most  unexpected  result  was  the  large  amount  of 
leakage  past  the  valve  from  the  steam-chest  into  the  exhaust. 
This  was  determined  by  blocking  up  the  ports  with  lead  and 
running  the  valve  in  the  normal  manner  by  an  electric  motor. 
This  leakage  appeared  to  be  proportional  to  the  difference  of 
pressure  causing  the  leak,  and  to  be  independent  of  the  num- 
ber of  reciprocations  of  the  valve  per  minute.  From  the  tests 
thus  made  on  the  leakage  to  the  exhaust,  the  leakage  correc- 
tion in  Table  IX  was  estimated.  Although  the  investigators 
concluded  that  their  experimental  rate  of  leakage  was  quite 
definite,  it  would  appear  that  much  of  the  discrepancy  between 
the  indicated  and  calculated  condensation  and  vaporization 
can  be  attributed  to  this  correction,  which  was  two  or  three 
times  as  large  as  the  weight  of  steam  passing  through  the 
cylinder.  Under  the  most  favorable  condition  (for  the 
seventh  test)  the  leakage  was  0.0494  of  a  pound  per  stroke, 
and  since  there  were  97  strokes  per  minute,  it  amounted  to 

0.0494  X  97  X  60  —  287.5 

pounds  per  hour,  or  32.6  pounds  per  horse-power  per  hour, 
so  that  the  steam  supplied  per  horse-power  per  hour  amounted 
to  56.4  pounds.  If  it  be  assumed  that  the  horse-power  is 
proportional  to  the  number  of  revolutions,  then  the  engine 


INFLUENCE    OF   THE    CYLINDER    WALLS.  351 

running  double-acting  will  develop  about  44  horse-power  per 
hour,  and  the  leakage  then  would  be  reduced  to  6.5  pounds 
per  horse-power  per  hour.  Such  a  leakage  would  have  the 
effect  of  increasing  the  steam-consumption  from  23.5  to  30 
pounds  of  steam  per  horse-power  per  hour. 

To  substantiate  the  conclusions  just  given  concerning  the 
leakage  to  the  exhaust,  the  investigators  made  similar  tests 
on  the  leakage  of  the  valves  of  a  quadruple-expansion  engine, 
which  had  plain  unbalanced  slide-valves.  The  valves  chosen 
were  the  largest  and  smallest ;  both  were  in  good  condition, 
the  largest  being  absolutely  tight  when  at  rest.  Allowing 
for  the  size  and  form  of  the  valve  and  for  the  pressure,  sub- 
stantially identical  results  were  obtained. 

The  following  provisional  equation  is  proposed  for  calcu- 
lating the  leakage  to  the  exhaust  for  slide-valves: 

kip 
leakage  =  — , (307) 

where  /  is  the  lap  and  e  is  the  perimeter  of  the  valve,  both  in 
inches,  and  /  is  the  pressure  in  pounds  in  the  steam-chest  in 
excess  of  the  exhaust  pressure.  The  valve  of  the  constant  in 
equation  (307)  is  0.021  for  the  high-speed  engine  used  by 
Callendar  and  Nicolson,  and  is  0.019  f°r  one  test  each  of  the 
valves  for  the  quadruple  engine,  while  another  test  on  the 
large  valve  gave  0.021. 

This  matter  of  the  leakage  to  the  exhaust  is  worthy  of 
further  investigation.  Should  it  be  found  to  apply  in  general 
to  slide-valve  and  piston-valve  engines  it  would  go  far  towards 
explaining  the  superior  economy  of  engines  with  separate 
admission-  and  exhaust-valves,  and  especially  of  engines  with 
automatic  drop-cut-off  valves  which  are  practically  at  rest 
when  closed.  It  may  be  remarked  that  the  excessive  leakage 
for  the  engine  tested  appears  to  be  due  to  the  size  and  form 
of  valves.  The  valve  was  large  so  as  to  give  a  good  port- 
opening  when  the  cut-off  was  shortened  by  the  fly-wheel 
governor,  and  was  faced  off  on  both  sides  so  that  it  could  slide 


35 2  THERMODYNAMICS   OF   THE   ST2AM-ENGINE. 

between  the  valve-seat  and  a  massive  cover-plate.  The  cover- 
plate  was  recessed  opposite  the  steam-ports,  and  the  valve  was 
constructed  so  as  to  admit  steam  at  both  faces;  from  one  the 
steam  passed  directly  into  the  cylinder  and  from  the  other  it 
passed  into  the  cover-plate  and  thence  into  the  steam-port. 
This  type  of  valve  has  long  been  used  on  the  Porter-Allen 
and  the  Straight-line  engines;  the  former,  however,  has 
separate  steam-  and  exhaust-valves.  Such  a  valve  has  a  very 
long  perimeter  which  accounts  for  the  very  large  effect  of  the 
leakage. 

Messrs.  Callendar  and  Nicolson  consider  that  the  leakage 
is  probably  in  the  form  of  water  which  is  formed  by  conden- 
sation of  steam  on  the  surface  of  the  valve-seat  uncovered  by 
the  valve,  and  say  further,  that  it  is  modified  by  the  condi- 
tion of  lubrication  of  the  valve-seat  as  oil  hinders  the  leakage. 


CHAPTER    XV. 
ECONOMY   OF   STEAM-ENGINES. 

THE  importance  and  the  intricacy  of  the  action  of  the 
walls  of  the  cylinder  of  a  steam-engine  have  thus  far  prevented 
any  formulation  of  the  actual  economy  of  steam-engines.  It 
therefore  is  necessary  to  make  a  study  of  steam-engine  tests^ 
to  learn  the  conditions  favorable  to  economy  and  to  determine 
ihe  effects  of  various  devices  and  methods  employed  for  the 
purpose  of  improving  economy. 

Table  X  gives  the  economy  of  various  types  of  engines,, 
and  represents  the  present  state  of  the  art  of  steam-engine 
construction.  It  must  be  considered  that  in  general  the 
various  engines  for  which  results  are  given  in  the  table  were 
carefully  brought  up  to  their  best  performance  when  these 
tests  were  made.  In  ordinary  service  these  engines  under 
favorable  conditions  may  consume  five  or  ten  per  cent  more 
steam  or  heat ;  under  unfavorable  conditions  the  consumption 
may  be  half  again  or  twice  as  much. 

All  the  examples  in  the  table  are  taken  from  reliable 
tests:  a  few  of  these  tests  are  stated  at  length  in  the  chapter 
on  the  influence  of  the  cylinder- walls;  others  are  taken  from 
various  series  of  tests  which  will  be  quoted  in  connection  with 
the  discussion  of  the  effects  of  such  conditions  as  steam- 
jacketing  and  compounding;  the  remaining  tests  will  be  given 
here,  together  with  some  description  of  the  engines  on  which 
the  tests  were  made. 

The  first  engine  named  in  the  table  is  at  the  Chestnut  Hill 
pumping-station  for  the  city  of  Boston.  Its  performance  is. 

353 


354 


THERMODYNAMICS    OF    THE   STEAM-ENGINE. 


TABLE  X. 

EXAMPLES    OF   STEAM-ENGINE    ECONOMY. 


Type  of  Engine. 

Revolutions  per 
minute. 

Steam-pressuie. 
pounds  per 
square  inch. 

Horse-power. 

Steam  per  horse- 
power per  hour. 
Pounds 

U 

OS 

ll 

R! 

^F. 

03 

Coal  per  horse- 
power per  hour, 
pounds. 

Triple-expansion  engines: 
Leavitt   pumping  -  engine   at  Chestnut 
Hill                     

50  .  6 

176 

06 

II    2 

1  .  15 

Sulzer  mill-engine  at  Augsburg  
Allis  pumping-engine  at  Milwaukee.... 

56 
20.3 

•784. 

149 
122 
I7O 

1823 
574 

•7Q 

"•3 
n.  8 

12.7 

&vi\ 

218 

I.I9 

1.25 

Experimental  engine  at  the  Massachu- 
setts Institute  of  Technolgy  

92 
61 

147 

T6c 

125 

6,1  C 

13-7 

TO      4 

231 

1  .46 

72 

\A  e 

IOQJ. 

T  C      O 

2  .OI 

(Jo               Brookline  

Q4. 

I  ^J. 

1  136 

TC  .  C 

26-? 

2 

Compound  engines  : 
Leavitt  pumping-engine  at  Louisville.  . 
Leavitt     pumping  -  engine     at     Boston 
main-drainage  pumping-station  

18.6 

13-2 
76 

137 

99 

I  <^Q 

643 
252 

CQC 

12.2 

13-9 

TO 

222 

i-33 

80 

O2 

78 

16  9 

7  r 

60 

266 

8  4 

2    4.^ 

=;6 

<jy 
C7 

071 

21    2 

2  66 

Simple  engines,  condensing  : 
Corliss  engine  at  Creusot        

60 

84 

176 

16  Q 

do               without  jacket.  ....... 

CQ 

6l 

TCQ 

18.1 

Harris-Corliss  engine  at  Cincinnati.  .  •  . 

76 

O6 

1AC. 

IQ  .  A. 

Marine  engine  Gallcitin              

ci 

70 

1  80 

2O.  5 

60 

60 

2CQ 

Simple  engines,  non-condensing  : 

61 

UV 

•"Dy 

178 

^i  -y 

22    I 

61 

78 

2OQ 

24..  2 

Harris-Corliss  engine  at  Cincinnati.  .  .  . 

76 
126 

96 
I  2O 

120 

8O 

23-9 
oe    6 

•2  .  qc 

Harris-Corliss  engine  at  the  Massachu 
setts  Institute  of  Technology  

61 

77 

16 

T''       C 

CJ4.8 

Direct-acting  steam-pumps  : 
Fire-pump  at  the  Massachusetts  Insti- 
tute of  Technology       .  .  . 

*QO 

4.7 

4.1 

67 

1  1  IO 

do.                 at  reduced  power  
Steam-  and   feed-pump   on  the  Minne- 

*50 
*n 

59 

6.8 

8  8 

125 

QI 

2070 



do                  at  reduced  power 

*2    6 

i  6 

2J.T, 

*  Strokes  per  minute. 


ECONOMY  OF  Sl^EAM-ENGINES.  355 

the  best  known  to  the  writer  for  engines  using  saturated 
steam.  Some  engines  using  superheated  steam  have  a  less 
steam-consumption  than  this  engine,  but  their  economy  is  not 
given  here  for  reasons  which  will  appear  in  the  discussion  of 
the  use  of  superheated  steam.  This  engine,  which  was 
designed  by  Mr.  E.  D.  Leavitt,  has  three  vertical  cylinders 
with  their  pistons  connected  to  cranks  at  120°.  Each  cylinder 
has  four  gridiron  valves,  each  valve  being  actuated  by  its  own 
cam  on  a  common  cam-shaft ;  the  cut-off  for  the  high-pressure 
cylinder  is  controlled  by  a  governor.  Steam-jackets  are 
applied  to  the  heads  and  barrels  of  each  cylinder,  and  tubular 
reheaters  are  placed  between  the  cylinders.  Steam  at  boiler- 
pressure  is  supplied  to  all  the  jackets  and  to  the  tubular 
reheaters. 

TABLE  XI. 

TRIPLE-EXPANSION    LEAVITT    PUMPING-ENGINE   AT   THE 
CHESTNUT    HILL   STATION,  BOSTON,  MASSACHUSETTS. 

CYLINDER    DIAMETERS    13.7,    24.375,    AND    39    INCHES;    STROKE   6    FEET. 

By  Professor  E.  F.  MILLER,  Technology  Quarterly,  vol.  ix,  p.  72. 

Duration,  hours 24 

Total  expansion 21 

Revolutions  per  minute 5O.6 

Steam-pressure  above  atmosphere,  pounds  per  square  inch 175-7 

Barometer,  pounds  per  square  inch 14.9 

Vacuum  in  condenser,  inches  of  mercury 27.25 

Pressure  in  high  and  intermediate  jacket  and   reheaters,  pounds 

per  square  inch 175-7 

Pressure  in  low-pressure  jacket,  pounds  per  square  inch 99.6 

Horse-power 575-7 

Steam  per  horse-power  per  minute,  pounds 11.2 

Thermal  units  per  horse-power  per  minute 204.3 

Thermal  efficiency  of  engine,  per  cent 20.8 

Efficiency  for  non-conducting  engine,  per  cent 28.0 

Ratio  of  efficiencies,  per  cent 74 

Coal  per  horse-power  per  hour,  pounds 1.146 

Duty  per  1,000,000  B.  T.  u 141,855,000 

Efficiency  of  mechanism,  per  cent 89.5 

The  Sulzer  engine  at  Augsburg  has  four  cylinders  in  all, 
a  high-pressure,  an  intermediate,  and  two  low-pressure  cylin- 


356 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


ders.  The  high-pressure  cylinder  and  one  low-pressure 
cylinder  are  in  line,  with  their  pistons  on  one  continuous  rod, 
and  the  intermediate  cylinder  is  arranged  in  a  similar  way 
with  the  other  low-pressure  cylinder.  The  engine  has  two 
cranks  at  right  angles,  between  which  is  the  fly-wheel,  grooved 
for  rope-driving.  Each  cylinder  has  four  double-acting 
poppet-valves,  actuated  by  eccentrics,  links,  and  levers  from 
a  valve-shaft.  The  ad  mission- valves  are  controlled  by  the 
governors.  Four  tests  were  made  on  this  engine,  as  recorded 
in  Table  XII. 

TABLE  XII. 

TRIPLE-EXPANSION    HORIZONTAL   MILL-ENGINE. 

CYLINDER    DIAMETERS    29.9,    44-5,    AND    TWO    OF    $1.6    INCHES;    STROKE  78.7 

INCHES. 

Built  by  SULZER  of  Winterthur,  Zeitschrift  desVereins  Deutscher  Ingenieure, 

vol.  xl,  p.  534- 


I 

II 

III 

IV 

306 

022 

272 

•527 

c6.23 

56.28 

<?6.l8 

56.18 

Steam-pressure,  pounds  per  square  inch 
Vacuum    inches  of  mercury  

145-4 
27  .  24. 

147.9 

27.  2O 

148.4 
27.2O 

149-0 

27.  IQ 

1872 

i8-?< 

1850 

1821 

Steam  per  horse-power  per  hour,  pounds 
Mean  for  four  tests  11.46  
Coal  per  horse-power  her  hour,  pounds. 
Mean  for  four  tests  1.30  

n-53 
i-37 

8.78 

11.49 

1.36 

8.40 

11.49 
1.29 
8.  07 

u-33 
1.19 
9.62 

In  this  connection  there  is  given  in  Table  XIII  the  details 
of  five  tests  made  on  an  engine  by  the  same  builders,  but  of 
smaller  size  and  having  but  three  cylinders.  The  high-pres- 
sure and  intermediate  pistons  are  on  one  continuous  piston- 
rod  and  the  low-pressure  piston  is  on  a  separate  rod.  The 
engine  has  two  cranks  at  right  angles  and  a  fly-wheel  between 
them. 

The  details  of  the  test  on  the  Milwaukee  pumping-engine 
are  given  in  Table  VI  on  page  332.  The  engine  has  three 


ECONOMY   OF  STEAM-ENGINES. 


357 


vertical  cylinders  with  their  pistons  connected  to  cranks  at 
120°.  The  valve-gear  is  of  the  Corliss  type,  controlled  by  a 
governor. 

TABLE  XIII. 

TRIPLE-EXPANSION    HORIZONTAL   MILL-ENGINE   AT 
AUGSBURG. 

CYLINDER  DIAMETERS   11.28,   17-75,  AND  27. 6l  INCHES;    STROKE  39-37  INCHES. 

By  Professor  M.  SCHROTER,  Zeitschrift  des  Vereins  Deutscher  Ingenieure, 
vol.  xxxiv,  p.  7. 


I 

II 

III 

IV 

V 

Duration    minutes          

•701 

106 

•5-7O 

•3QT 

o26 

Revolutions  per  minute  

7O    S 

7O.  2 

7O    T 

76  •* 

7O   J. 

Cut-off  high-pressure  cylinder  

O.  25Q 

O.  252 

O.  25Q 

o  308 

o  300 

2?    6 

26.  q 

25.6 

21    5 

22    I 

Steam-pressure,  pounds  per  square  inch 
above  atmosphere  

IAS.  .6 

14.6-4 

147.6 

I5O.6 

14^  •  2 

Barometer    pounds  per  square  inch    ..    . 

T«I      Q 

T-l      Q 

jo    8 

TO       8 

T-I       Q 

Back  -  pressure,     absolute,     pounds    per 
square  inch          

I  .  I 

1.2 

1  .  1 

I    2 

1J-  V 
I    1-. 

Condensation    in   jackets   in  per  cent  of 
total  steam-consumption  

16.1 

20.  o 

18.  1 

17  .O 

18  i 

Condensation  withdrawn  from  first    in- 
termediate receiver,  per  cent  

2.  7 

2.Q 

2.7 

3  •  o 

2.2 

Horse-power               

TQC      O 

108  i 

108  i 

222    5 

212    8 

Steam  per  horse-power  per  hour,  pounds 
B.  T.  U.  per  horse-power  per  minute.... 

12.  6l 
226 

12.20 
221 

12.92 
230 

12-72 
227 

12-94 
230 

The  test  on  the  Willans  engine  is  taken  from  Table  XLII 
on  page  406.  This  remarkable  engine,  though  of  small  size 
and  power,  gives  an  exceedingly  good  economy  and  is  adapted 
to  driving  high-speed  machinery  directly.  The  three  pistons 
are  arranged  on  one  rod  and  are  single-acting.  The  under 
sides  of  the  high-pressure  and  the  intermediate  pistons  form 
the  tops  of  the  intermediate  receiver-spaces,  so  that  in  a 
manner  the  expansion  has  five  stages. 

The  test  on  the  experimental  engine  at  the  Massachusetts 
Institute  of  Technology  is  quoted  here  because  its  efficiency 
and  economy  are  chosen  for  discussion  in  Chapter  XI. 
Taking  its  performance  as  a  basis,  it  appears  on  page  248  that 


358 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


with  150  pounds  boiler-pressure  and  1.5  pounds  absolute 
back-pressure  an  engine  may  be  expected  to  give  a  horse- 
power for  11.5  pounds  of  steam,  from  which  it  appears  that 
under  its  conditions  its  performance  compares  favorably  with 
the  Sulzer  engine  or  even  the  Leavitt  engine. 

TABLE  XIV. 

MARINE-ENGINE    TRIALS. 

By  Professor  ALEXANDER  B.  W.  KENNEDY,  Proc.  Inst.  Meek.  Engs.,  1889- 
1892  ;  summary  by  Professor  H.  T.  BEARE,  1894,  p.  33. 


rt 

B 

rt 

> 

1 

Colchester. 

8 

„! 

•0  0 
juQ 

> 

Meteor. 

rt 
§ 

c. 

27.4 

C. 

30 

C. 

50.1 

T. 

29.4 

44 
70.1 

48 

17 

10.6 

71.8 

145.2 

2-73 
3-3 
1994 
15-0 
265 

2.OI 

7.46 

439 

T. 
21.9 
34 

57 
39 
16 
19.0 
61.1 

165 

0.70 

1.8 
645 

13-4 
250 
1.46 

9-15 
701 

50.3 

33 
14 
6.1 
55-6 

56.8 

2.32 
3-8 
37i 

21  .2 

380 

2.66 
7.96 
603 

57 
36 
10.9 
6.1 
86 

80.5 

2-51 
3-4 

IO22 
21.7 
393 
2.9 

7-4^ 

448 

97-1 

72 

9 

5-7 
36 

105.8 

4.72 
6.0 
2977 

20.8 

367 
2-3 

8.97 
272 

Steam-pressure  above  atmosphere,  pounds  per 

Pressure   in   condenser,    absolute,    pounds    per 
sqare  inch  ....          

Back-pressure,  absolute,  pounds  per  sq.  in.  ... 

Steam  per  horse-power  per  hour,  pounds  
Thermal  units  per  horse-  power  per  minute  

Weight  of  machinery  per  horse-power,  pounds. 

The  engines  of  the  S.  S.  lona  have  an  unusually  large 
expansion  and  give  a  correspondingly  good  economy.  The 
engines  of  the  Meteor  and  of  the  Brookline  give  the  usual 
economy  to  be  expected  from  medium-sized  marine  engines. 
Table  XIII  gives  details  of  tests  on  the  engines  of  the  two 
first  ships  mentioned,  together  with  tests  on  compound 
marine  engines.  Table  XV  gives  tests  on  the  engine  of  the 
Brookline.  It  appears  probable  that  the  relatively  poor 


ECONOMY   OF  STEAM-ENGINES. 


359 


economy  of  marine  engines  compared  with  stationary  engines 
is  due  to  the  smaller  degree  of  expansion,  which  is  accepted 
to  avoid  using  large  and  heavy  engines. 

TABLE   XV. 

TESTS  ON  THE  ENGINE  OF  THE  S.  S.  BROOKLINE. 

CYLINDER    DIAMETERS  23,   35,  AND    57    INCHES  ;    STROKE  36    INCHES. 

By  F.  T.  MILLER  and  R.  G.  B.  SHERIDAN,  Thesis,  1895,  M.I.T. 


I 

II 

III 

IV 

v 

2 

2 

j 

*1 

2i 

o<i  6 

0-3  5 

*I 

Steam-pressure,  pounds  per  square  inch  above 

T  e  c 

VJ-U 

je  e 

T  e  < 

yj 

TJ.K 

V.? 

T    .8 

Vacuum    inches  of  mercury  .        ... 

21    6 

21    O 

22    2 

21    7 

Horse-power   ••• 

12-12 

1221 

11^6 

1  1  ^7 

1148 

Steam  per  horse-power  per  hour,  pounds  
Coal  per  horse-power  per  hour,  pounds  

17-2 
2.22 
2O2 

16.9 
2.17 

288 

15-5 
1-99 
26^ 

I7.O 
2.18 

288 

16.3 
2.09 

277 

TABLE   XVI. 

COMPOUND    LEAVITT    PUMPING-ENGINE    AT   LOUISVILLE, 
KENTUCKY. 

CYLINDER    DIAMETERS  27.2    AND    54-1    INCHES  J    STROKE  IO    FEET. 

By  F.  W.  DEAN,  Trans.  Am.  Soc.  Mech.  Engs.,  vol.  xvi,  p.  169. 


Duration,  hours 

Revolutions  per  minute 

Pressure,  pounds  per  square  inch  : 

Barometric 

Boiler  above  atmosphere 

At  engine  above  atmosphere 

Back-pressure,  1.  p.  cylinder 

Total  expansions 

Moisture  in  steam,  per  cent 

Horse-power 

Steam  per  horse-power  per  hour,  pounds. 

B.  T.  U.  per  horse-power  per  minute 

Thermodynamic  efficiency,  per  cent 

Mechanical  efficiency,  per  cent 


144 
18.6 

14.6 
140 
137 
o.95 

20 

0-55 
643-4 

12.2 
222 
19 

93 


The  best  performance  of  a  compound  engine  using  satu- 
rated steam,  which  is  known  to  the  writer,  is  that  reported 
for  a  pumpmg-engine  at  Louisville,  Ky.  This  engine  has 


360 


THERMOD  YNAM2CS   OF    THE   SJ^EAM-ENGINE. 


two  cylinders,  each  jacketed  with  steam  at  boiler-pressure  on 
barrels  and  heads  and  steam  at  the  same  pressure  is  used  in  a 
tubular  reheater.  Each  cylinder  has  four  gridiron  valves 
actuated  by  as  many  cams  on  a  cam-shaft.  The  details  of 
the  test  are  given  in  Table  XVI,  and  Table  XVII  gives  two 
tests  on  another  compound  Leavitt  engine  at  the  Boston 
main-drainage  pumping-station.  A  comparison  of  the  two 
tables  shows  the  advance  made  in  ten  years  from  1885  to 
1895. 

TABLE   XVII. 

LEAVITT   COMPOUND    PUMPING  ENGINE    AT  THE    BOSTON 
MAIN  DRAINAGE   WORKS. 

CYLINDER    DIAMETERS  25.5    AND    $2    INCHES  ;    STROKE  9    FEET. 


Duration,  hours  and  minutes 

Revolutions  per  minute 

Boiler-pressure  above  atmosphere,  pounds  per  square  inch. . 

Vacuum,  inches  of  mercury 

Barometer,  inches  of  mercury 

Horse-power 

Steam  per  horse-power  per  hour,  pounds 

Coal  per  horse-power  per  hour,  pounds 

Steam  per  pound  of  coal,  from  and  at  212°  F 

Duty,  work  per  100  pounds  of  coal,  millions  of  foot-pounds.., 


24-43 
13-17 
99-4 
28.1 
30.18 
251-5 
13-9 
1-33 

12.12 
122.5 


24-3? 
13.42 
98.6 
28.0 
29.81 
290.2 
14.2 

1-35 
11.83 
122.4 


TABLE   XVIII. 

CROSS-COMPOUND    MILL-ENGINE   AT   NATICK,  R.  I. 

CYLINDER    DIAMETERS   18.4   AND    48.5    INCHES  |    STROKE  4    FEET. 

By  F.  W.  DEAN,  Trans.  Am.  Soc.  Meek.  Engs.,  vol.  xvi,  p.  179. 


I 

II 

4C 

e 

76   d. 

76  6 

.•Steam-pressure  above  atmosphere,  pounds  per  square  inch.  . 

159 

oe    A 

158 

otr    o 

oq 

•J-J      A 

I    O 

i  8 

i  .y 
CoC 

ego 

3V5 

TO 

TO      0 

The    compound    mill-engine    at   Nattck,   R.   I.,    has    two 
cylinders  with  their  pistons  acting  on  cranks  at  right  angles. 


ECONOMY  OF  STEAM-ENGINES.  361 

The  valves  are  of  the  gridiron  type  as  made  by  the  Wheelock 
Engine  Company.  The  high-pressure  cylinder  is  jacketed  on 
the  heads  and  barrel;  the  low-pressure  cylinder  is  jacketed 
on  the  heads  only.  A  reheater  is  placed  between  the  cylin- 
ders. A  notable  feature  of  this  engine  is  the  ratio  of  the 
volume  of  the  cylinder, 


48.5    :   18.4    1:7:1, 

which  gives  a  large  number  for  the  total  expansion  without 
requiring  a  very  early  cut-off  for  the  high-pressure  cylinder. 

Table  XIX  gives  tests  on  another  cross-compound  engine 
which  has  a  cylinder  ratio  of  three  and  a  half  to  one,  and 
which  has  neither  steam-jackets  nor  reheater,  and  which  has 
nevertheless  nearly  as  good  an  economy. 

TABLE   XIX. 

CROSS-COMPOUND   MILL-ENGINE  AT   NEW   BEDFORD,  MASS. 

CYLINDER    DIAMETERS  30    AND    $6    INCHES  J    STROKE  72    INCHES. 

By  DENTON,  JACOBUS,  and    RICE,    Trans.  Am.   Soc.  Mech.  Engs.,  vol.  xv, 

p.  882. 

Revolutions  per  minute 65.2 

Steam-pressure  above  atmosphere,  pounds  per  square  inch 123.0 

Vacuum,  inches  of  mercury 25.6 

Total  expansions 13.4 

Superheating  at  throttle,  degrees  F 14.6 

Horse-power 1592 

Steam  per  horse-power  per  hour,  pounds 13.5 

Coal  per  horse-power  per  hour,  pounds i£ 

B.  T.  U.  per  horse-power  per  minute 247 

Table  XX  gives  tests  on  an  engine  built  by  the  same 
makers  as  that  for  which  tests  are  recorded  in  Table  XVIII. 
This  engine  has  three  cylinders  with  a  ratio  of  seven  to  one 
for  the  volumes  of  the  largest  and  smallest  cylinders.  In  two 
of  the  tests  the  engine  was  run  as  a  compound  engine  using 
only  the  smallest  and  largest  cylinders;  in  the  other  two  tests 
the  three  cylinders  were  used  as  designed.  The  engine  has 
jackets  on  the  heads  and  barrels  of  the  high-pressure  and 


362 


THERMODYNAMICS    OF   THE   STEAM-ENGINE. 


intermediate  cylinders  and  on  the  heads  of  the  low-pressure 
cylinder.  A  further  consideration  of  these  tests  will  come  in 
connection  with  the  discussion  of  compound  and  triple- 
expansion  engines. 

TABLE  XX. 

HORIZONTAL   MILL-ENGINE    AT    HOLYOKE,  MASS. 

DIMENSIONS:    HIGH-PRESSURE  CYLINDER,  12  IN.  DIAMETER,  36  IN.  STROKE; 
INTERMEDIATE  CYLINDER,  l6  IN.  DIAMETER,  36  IN.  STROKE; 
LOW-PRESSURE  CYLINDER,  24||  IN.  DIAMETER,  48  IN.  STROKE. 

Tested  by  S.  M.  GREEN  and  G.  I.  ROCKWOOD,  Trans,  Am.  Soc.  Mech.  Engs., 

vol.  xiii,  p.  647. 

The  engine  was  run  with  large  and  small  cylinders  only,  and  with  all 
three. 


I 

II 

III 

IV 

Compound. 

Triple. 

5 
79.2 

142 

13 
187.1 

13-4 

5 
79-3 

142 

14 
180.7 

13-1 

5 
79-0 

142 
16 
199.1 
13.0 

5 
79.0 

M3 
16 
178.2 
13-3 

Steam-pressure  above  atmosphere,  pounds 

Per  cent  of  steam  used  in  jackets 

Horse-power   .... 

Steam  per  horse-power  per  hour,  pounds. 

Table  XXI  gives  four  tests  on  a  small  portable  engine 
which  gives  a  very  good  economy  for  its  type  and  size. 

The  details  of  the  tests  on  the  Rush  and  the  Fust  Yama 
are  given  in  Table  XXXII  and  XIV  on  pages  256  and  358. 

A  remarkably  complete  and  important  series  of  tests  was 
made  in  1884  by  M.  F.  Delafond.  These  tests  are  recorded 
in  Tables  XXX  and  XXXI,  from  which  there  are  quoted  in 
Table  X  four  results  with  and  without  condensation  and  with 
and  without  steam  in  the  jackets. 

The  details  of  the  tests  on  the  Harris-Corliss  engine  at 
Cincinnati,  together  with  tests  on  two  similar  engines,  are 
given  in  Table  XXII. 


ECONOMY   OF  ^TEAM-ENGINES. 


363 


TABLE  XXI. 

PORTABLE   COMPOUND    CONDENSING-ENGINE. 

Tested  by  a  Committee  of  the  Soc.  Ind.  DE  MULHOUSE,  1879. 

Reported  by  ISHERWOOD,  Jour.  Franklin  Jnst.,  vol.  cxx. 


i 

II 

in 

IV 

q 

A 

324. 

80 

88  5 

oo 

88.7 

Cut-off    small  cylinder          ...        

O   J.2 

O.12 

OOC 

OJ.2 

Total  expansions  .  .          

6  26 

6  26 

9.64 

6  26 

Steam-pressure  above  the  atmosphere, 
Ibs    per  sq    in  

QI  .8 

QI    5 

QT  •  7 

Q2    2 

Atmospheric  pressure,  Ibs.  per  sq.  in... 

14.2 
21 

14.2 

2       A 

14.2 
24 

14-2 
2j 

Horse-power    indicated                         ••    • 

77    2 

77   6 

6^    Q 

77    8 

Horse-power  by  brake     .  .                    ... 

67   7 

67  «; 

e  e    7 

67    « 

Steam  per  I  H  P.  per  hour  Ibs       

17    7 

17    ^ 

l6.Q 

16  Q 

B   T    U.  per  horse-power  per  hour  

Ti8 

*27 

^18 

•7IC 

TABLE  XXII. 

AUTOMATIC    CUT-OFF    ENGINES. 

CYLINDER    DIAMETERS    l8    INCHES;    STROKE    4    FEET. 

By  J.  W.  HILL. 
(First  Millers'  International  Exhibition,  Cincinnati,  1880.) 


Condensing. 

Non-condensing. 

R. 

H. 

W. 

R. 

H. 

W. 

Duration         .... 

10 
0.124 
75-4 
95-8 
29-7 
25-5 
4-5 
J43-2 

20.6 

372 

10 

0.119 
75-8 
96.1 
29.6 
25-7 
3-4 
I45-I 
19.4 
349 

10 

0.131 

74-5 
96.3 
29.4 
24.0 
4-7 
143-9 
»9-S 
343 

0.160 

75-3 
96.6 
29.8 

10 

0.136 

5ii! 

29.6 

1     10 
0.170 
76.1 
96-3 
29-5 

Cut-off 

Revnlutions  per  minute      .       .         .... 

Boiler-pressure  above  atmos.,  Ibs.  per  sq.  in. 
Barometer,  inches  of  mercury  

Vacuum,  inches  of  mercury                       ... 

Back-pressure,  absolute,  Ibs.  per  sq.  in.... 
Horse-power  
Steam  per  horse-power  per  hour,  pounds.. 
B.  T.  U.  per  horse-power  per  hour  

»5-5 
121.7 
25-9 
433 

14.9 
119.7 

23-9 
400 

'I'5 
126.7 

24.9 
4i5 

The  tests  on  the  engine  of  the  Gallatin  are  taken  from 
Table  XXXII  on  page  388. 

Table  XXIItf  gives  the  details  of  a  test  on  a  Hoadley 
portable  engine  which  had  a  piston-valve  controlled  by  a  fly- 
wheel governor,  made  by  Mr.  Hoadley  in  1876. 


364 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


TABLE  XXII*. 

HOADLEY    PORTABLE    ENGINE. 

CYLINDER    DIAMETER    14.56    INCHES;    STROKE    28.5  INCHES. 

Duration  of  test 6  hrs.  2  min. 

Revolutions  per  minute 125.96 

Steam-pressure  in  boiler,  pounds 120 

Cut-off,  per  cent 17 

Horse-power  by  indicator 80.29 

Horse-power  by  brake 72.72 

Friction  of  engine,  horse-power 7.57 

Horse-power  by  indicator  without  load 5.80 

Steam  per  I.H.P.  per  hour,  weighed,  pounds 25.61 

"          "    brake  H.P.  per  hour,  weighed,  pounds...  28.27 
Coal  per  indicated  horse-power  per  hour,  pounds. . .       3.35 

"       "     brake  horse-power  per  hour,  pounds 3.69 


TABLE  XXIII. 

DUPLEX    DIRECT-ACTING     FIRE-PUMP    AT    THE    MASSACHU- 
SETTS   INSTITUTE   OF   TECHNOLOGY. 

TWO    STEAM-CYLINDERS    l6    INCHES    DIAMETER,    12    INCHES    STROKE. 

Technology  Quarterly,  vol.  viii,  p.  19. 


1 

Q 

M 

V 

^ 

flj 

E 
6 

id 

5 

0 

"O 

"O 

B 

i_, 

3 

J    C 

u_C 

rt  ^ 

^c  o 

*•*  u     . 

1« 

"o 

*0 

1 

ll 

If 

1- 

II 

tp 

v  3 

s 

-8 

JS 

S  31 

S^  w 

r| 

g{ 

t>  w 

5^ 

sjj 

|  S) 

u  -S 
OC/3 

5^ 

rt  0 

«  a 

H.  a 

38.5 

c/5 

J 

"* 

C/3 

K 

ffi 

c^ 

CQ 

Q 

nn 

1  1  .  40 

IO.  IO 

g 

6.78 

125 

2O7O 

13  920,000 

yy 

1  1  .  70 

1  1  .  07 

55.6 

12    48 

A  ^  D 
IOI 

l674 

17,  540,000 

I  IQ 

1  1    4Q 

1  1  .  07 

A  £t  .  ^.<-> 

12.  l8 

A  W  /  ^T 
l8OO 

16  Q8o,ooo 

x  AV 
135 

ii  .ify 
II.60 

J.  J.   *  \J  / 

II.  10 

53-8 

18.24 



92 

AUWy 
1530 

19,850,000 

156 

10.90 

10.26 

47.2 

21.  OO 

19.80 

98 

l6l9 

18,280,000 

IO.O9 

IO.3I 

45  -6 

32    Q5 

78 

I2QI 

23,730,000 

175 

11-77 

II  •  7Q 

*T*?       v 

45  -6 

3Q-  55 

/  W 

66 

x  Ay* 

A  /  D 
1  8O 

*  *    /  / 

U74 

•*•  •*•    /  v 
11.66 

46  5 

O  V     O  3 
41  .  20 

67 

1  1  IO 

27  030  ooo 

•  It 

T1*-'  *    J 

"/ 

The  test  of  the  small  Harris-Corliss  engine  at  the  Massa- 
chusetts Institute  of  Technology  is  taken  from  Table  II  on 
page  318.  A  complete  calculation  for  the '  application  of 
Hirn's  analysis  to  this  test  is  given  on  page  313. 


ECONOMY   OF  STEAM-ENGINES. 


365 


The  two  tests  on  the  direct-acting  fire-pump  at  the 
Massachusetts  Institute  of  Technology  are  taken  from  Table 
XXIII,  and  the  tests  on  the  feed-  and  fire-pump  on  the 
Minneapolis  are  given  in  Table  XXIV.  Both  sets  of  tests 
show  the  extravagant  consumption  of  steam  by  such  pumps 
when  running  at  reduced  powers.  The  latter  table  is  most 
interesting  on  account  of  the  light  that  it  throws  on  the  way 
that  coal  is  consumed  by  a  war-vessel  when  cruising  at  slow 
speeds  or  lying  in  harbor. 

TABLE  XXIV. 

TESTS    OF   AUXILIARY    STEAM   MACHINERY    OF   THE  U.  S.  S. 

MINNEAPOLIS. 

By  P.  A.  Engineer  W.  W.  WHITE,  U.   S.   N.,  Journal  Am.   Soc.   Naval 

Engs.,  vol.  x. 


, 

•si 

5 

o  l- 

§ 

as 

i  A 

fc^ 

tT 

. 

£ 

w 

sg 

Engine  or  pump  tested.             °  £ 

1  l^ 

3  U 

Diam.  of  stea 
cylinders,  i 

Diam.  of  wat 

cylinders,  i 

Nominal  stro 
inches. 

1 

-5 

-  — 

I1 

Double  strok 
revolutions 
minute. 

Duration  of  t 

Indicated  hoi 
power. 

Steam  per  ho 
power  per  \ 

Centre  circulating-pump: 

5 

5 

3g 

6 

6 

oo 

rf 

Starboard  circulating-pump: 

5 

76 

6 

6 

82 

•1-28 

I2C 

16 

J 

16.6 

6  5 

Q-* 

Centre  air-pumpt   

16 

21 

15-2 

3-2 

25.2 

78 

_ 

Fire-  and  feed-pump       

12.7 

^J 

0.78 

6A 

ill 

do 

8  8 

do.                

12 

7-5 

12 

10.8 

2.6 

3_27 

243 

1  J. 

2     - 

Blower-engine  .... 

595 

l6.3 

6- 

do.             

10.5 

S 

5 

425 

0-26 

35-2 

S6 

Ice-machine  engine  . 

7 

IO 

IO 

73-  * 

5-^2 

6.0 

70 

*  One  cylinder  only  supplied  with  steam. 

t  Pump  loaded   with  three  times  the  power  developed  during  official  trial,  when  main 
engine  indicated  7219  H.  P. 

Effect  of  Raising  Steam-pressure. — A  study  of  the 
examples  of  steam-engine  economy  given  in  Table  X,  and  of 
the  details  of  the  tests  given  in  the  several  tables  referred  to, 
shows  that  in  general  a  gain  in  economy  is  to  be  obtained  by 
increasing  the  steam-pressure  and  the  total  number  of  expan- 


366 


THERMODYNAMICS   OF    THE   STEAM-ENGINE. 


sions.  This  general  statement  can  be  held  to  be  true  only 
when  the  proper  methods  are  used  to  ameliorate  the  effects  of 
cylinder-condensation  and  reevaporation,  which  have  already 
been  seen  to  place  a  very  strict  limit  on  the  number  of 
expansions  to  be  profitably  used  for  a  simple  steam-engine. 

It  is  interesting  here  to  investigate  the  effect  of  increasing 
the  steam-pressure  only,  for  a  non-conducting  engine,  with- 
out changing  the  expansion.  The  accompanying  table  gives 
the  efficiencies  for  such  an  engine  for  various  steam-pressures 
calculated  by  equation  (260),  page  248,  assuming  in  all  cases 
that  the  absolute  pressure  at  release  is  one-third  that  during 
admission. 

TABLE  XXV. 


I 

II 

III 

IV 

Pressure,  pounds  per  square  inch: 
By  R<mfire  during  admission  

an    7 

60  "\ 

OO    1 

4.C 

7c 

IO<i 

I-ie 

At  end  of  expansion  

TC 

oc 

•7  e 

AC 

Back-pressure  

Id.  7 

14..  7 

Id.    7 

IJ.    7 

Quality  of  steam  at  release  

O.  Qd8 

o  .  036 

OOa/1 

Efficiency  

0.085 

O    III 

o  123 

w>  VJJ 

OTT-J 

B.  T.  U.  per  horse-power  per  minute.... 
Steam  per  horse-power  per  hour,  pounds 

499 
30-4 

382 
22.6 

345 
20.7 

319 

19.0 

From  this  calculation  it  appears  that  there  is  at  first  a 
notable  gain  in  economy  from  increasing  the  steam-pressure 
without  changing  the  expansion  for  a  non-conducting  engine, 
but  that  after  a  moderate  pressure  has  been  reached  the 
gain  for  further  increase  is  small.  Now  the  actual  engine 
will  have  a  greater  steam-consumption  on  account  of  the  loss 
by  external  radiation,  and  the  loss  due  to  initial  condensa- 
tion, reevaporation,  and  exhaust-waste.  The  absolute  loss 
from  external  radiation  increases  with  the  steam-pressure, 
but  the  horse-power  of  the  engine  increases  more  rapidly; 
consequently  the  radiation  per  horse-power  decreases  as  the 
pressure  is  increased.  Since  the  changes  of  temperature  are 
larger  for  a  high  than  for  a  low  pressure,  it  is  a  reason- 


ECONOMY   OF  STEAM-ENGINES.  367 

able  inference  that  the  condensation  and  reevaporation  in 
the  cylinder,  and  the  exhaust-waste  are  liable  to  increase 
as  the  steam-pressure  is  raised.  We  may,  therefore,  expect 
to  find  that  tests  on  steam-engines  will  give  a  result  similar 
to  that  calculated  for  a  non-conducting  engine,  i.e.,  that 
with  fixed  expansion  there  will  be  at  first  a  considerable 
gain  from  raising  the  steam-pressure  in  a  simple  engine, 
but  that  beyond  a  moderate  steam-pressure  the  gain  will 
be  very  slow.  Some  tests  even  show  a  loss  from  raising  the 
steam-pressure  too  high. 

A  confirmation  of  the  ideas  just  enunciated  may  be  found 
in  Table  XXXVIII,  page  403,  which  gives  the  results  of 
tests  on  the  Willans  engine,  using  one  cylinder  only  as  a 
single-acting  simple  engine.  Tests  I  to  6  were  made  with  the 
cut-off  at  half  stroke  and  with  the  steam-pressure  varying  from 
64.7  to  20  pounds  absolute,  the  back-pressure  being  in  all 
about  one  pound.  Increasing  the  pressure  from  20  to  55 
pounds  absolute,  or  from  about  5  to  about  40  pounds  above 
the  atmosphere,  gave  a  gain  of  about  ten  per  cent,  but  a 
further  increase  to  64.7  pounds  absolute,  or  about  50  pounds 
by  the  gauge,  gave  a  distinct  loss.  A  similar  though  not  so 
pronounced  effect  is  shown  by  tests  7  to  12. 

A  more  striking  confirmation  is  given  by  tests  on  a  Corliss 
engine  at  Creusot  without  steam  in  the  jackets,  as  represented 
by  Tables  XXX  and  XXXI  on  pages  454  and  455  and  by 
Fig.  79.  In  the  figure  the  curves  lettered  C  represent  tests 
made  with  a  vacuum  and  curves  lettered  N  represent  tests 
without  a  vacuum.  The  figures  used  in  conjunction  with  the 
curves  give  the  approximate  boiler-pressure  for  tests  repre- 
sented. The  curves  representing  tests  with  condensation 
show  a  decided  gain  when  the  steam-pressure  is  raised  from 
35  pounds  to  50  pounds  above  the  atmosphere,  and  an 
appreciable  gain  for  a  further  increase  from  50  to  60  pounds. 
A  further  increase  to  80  and  100  pounds  is  accompanied 
by  a  distinct  loss.  The  tests  without  condensation  show  a 
large  gain  from  raising  the  pressure  from  50  to  75  pounds 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and  little  if  any  gain  from  a  further  increase  to  100  pounds 
above  the  atmosphere. 

Methods  of  Improving  Economy. — Bearing  in  mind  the 
fact  just  established  that  there  is  little  if  any  gain  in  economy 
to  be  obtained  by  raising  the  steam-pressure  beyond  a  certain 
very  moderate  limit  unless  the  expansion  may  be  increased 
at  the  same  time,  and  also  the  fact  that  the  economical  expan- 
sion for  a  simple  unjacketed  steam-engine  is  very  strictly 
limited  by  initial  condensation,  reevaporation,  and  exhaust- 
waste,  we  are  led  to  the  consideration  of  methods  for 
ameliorating  the  action  of  the  walls  of  the  cylinder.  Two  of 
these  have  been  considered  in  connection  with  the  study  of 
the  influence  of  the  cylinder-walls  in  the  preceding  chapter, 
namely,  the  use  of  superheated  steam  and  the  use  of  the 
steam-jacket.  Another  method  of  even  more  practical  im- 
portance is  the  use  of  compound  and  multiple-expansion 
engines.  Again,  reheaters  may  be  placed  between  the  cylin- 
ders of  compound  or  multiple-expansion  engines  to  dry  or 
superheat  the  steam  on  its  way  from  one  cylinder  to  another. 
Any  two  or  all  of  these  several  methods  may  be  used  in  con- 
junction. Examples  of  almost  all  of  the  possible  combinations 
may  be  found  in  practice,  and  the  advantages  to  be  obtained 
from  some  of  them  can  be  determined  from  tests  which  will 
now  be  studied  in  detail. 

Superheated  Steam. — The  most  direct  and  effective  way 
of  improving  steam-engine  economy  is  by  the  use  of  super- 
heated steam,  and  yet  no  permanently  good  results  have  been 
obtained,  on  account  of  the  practical  difficulties  of  maintaining 
the  superheating  apparatus.  Some  upright  boilers  give 
superheated  steam,  but  when  the  superheating  is  forced  to 
any  very  considerable  degree  they  are  likely  to  be  troubled  by 
wasting  of  the  upper  ends  of  the  tubes.  Whenever  super- 
heated steam  has  been  used  so  as  to  give  a  notable  gain  in 
economy  the  superheating  has  been  accomplished  in  a  separate 
apparatus,  which  has  taken  the  form  of  a  coil  of  pipe  exposed 
to  the  products  of  combustion  beyond  the  boiler.  Now  it  is 


ECONOMY  OF  STEAM-ENGINES.  369 

the  accepted  experience  of  boiler-makers  that  surfaces  exposed 
to  the  fire  must  be  of  moderate  thickness  or  they  will  rapidly 
waste  away.  Thus  it  is  not  desirable  to  make  furnace-flues 
more  than  half  an  inch  thick,  and  if  they  are  made  thicker 
they  are  liable  to  waste  away  till  they  are  reduced  to  about 
that  thickness.  Plates  and  tubes  if  thin  enough  endure  long 
service  in  a  boiler  when  exposed  to  the  fire  because  they  are 
kept  at  a  moderate  temperature  by  the  water  in  the  boiler. 
If  steam  is  to  be  superheated  strongly  in  a  coil  of  pipe  or 
other  device  which  is  exposed  to  hot  gases,  the  metal  of  the 
superheater  must  be  strongly  heated  and  is  sure  to  waste 
away  rapidly.  There  is  no  material  that  can  stand  long 
service  when  exposed  at  once  to  a  high  pressure  and  a  high 
temperature.  There  is  little  risk,  therefore,  in  predicting  that 
all  superheating  devices  now  used  will  eventually  be  discarded 
for  this  reason. 

From  the  considerations  just  stated  no  tests  with  super- 
heated steam  are  given  in  Table  X,  though  the  economy 
obtained  by  the  use  of  superheated  steam  is  remarkable,  both 
comparatively  and  absolutely.  Several  series  of  tests  on 
engines  using  superheated  steam  will  be  given,  together  with 
a  discussion  of  the  advantages  obtained  from  its  use. 

Tests  on  the  Eutaw. — The  U.  S.  S.  Eutaw  was  built  for 
special  service  in  1863-64,  and  had  a  single-cylinder  inclined 
engine  with  poppet-valves  and  a  Stevens  adjustable  cut-off. 
The  steam  from  the  boilers  could  be  supplied  directly  to  the 
engine  or  it  could  be  passed  through  a  coil  superheater  in  the 
uptake.  The  tests  were  made  at  the  dock,  the  speed  of  rotation 
being  controlled  by  removing  more  or  less  of  the  paddles  from 
the  paddle-wheels.  The  details  of  the  tests  are  given  in 
Table  XXVI.  Four  of  the  tests  are  with  saturated  steam 
and  five  are  with  superheated  steam.  The  best  result  with 
saturated  steam  is  obtained  for  a  cut-off  at  0.32  of  the  stroke, 
agreeing  with  the  conclusions  from  tests  on  the  Michigan 
(Table  I,  page  303).  The  tests  with  superheated  steam  show 
a  good  deal  of  irregularity,  which  cannot  be  satisfactorily 


OF  THK 

UNIVERSITY 


370 


THERMODYNAMICS    OF   THE   STEAM-ENGINE. 


accounted  for  either  by  the  degree  of  superheating  or  the 
perfection  of  the  vacuum.  A  comparison  of  the  best  result 
for  superheated  steam  with  the  best  result  for  saturated  steam 
shows  a  gain  in  steam  economy  of 

30.6  —  25.1 


30.6 


X  ioo  =  1 8  per  cent, 


and  a  gain  in  coal-consumption  of 
2.84  —  2.42 


2.84 


X  ioo  =  15  per  cent. 


TABLE  XXVI. 

TESTS    ON    THE   ENGINE    OF    THE    U.  S.  S.  EUTAW. 

CYLINDER    DIAMETER    4    FEET    IO    INCHES;     STROKE    8    FEET    9    INCHES. 

By  Chief  Engineer  ISHERWOOD,  Researches  in  Experimental  Steam 
Engineering. 


Saturated  steam. 

Superheated  steam. 

• 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

72 
0.24 

5-49 

40-3 
30 
27 

1.8 
*54-4 
39-6 
3-77 
56 

72 
0.32 
6.58 

40.6 

5.6 

*«3 

228.6 
30.6 
2.84 
37 

72 
0.50 
8.60 

40.9 

3° 
27.1 

1.6 

372-5 

32-7 
2.87 
3° 

72 
0.58 
9.19 

38.2 
29.7 
28 

0.9 
414.9 
3i-4 
2.90 
24 

72 
0.29 
6.48 

41.0 
30.1 
28 

i  .  i 
396 
207.3 

30.1 
2.84 
43 

72 
0.32 

6-55 

41.1 

3° 
26.2 

2-5 
366 
218.2 

29.2 
2.64 
37 

72 
0.50 

9.00 

41.7 
30 
26.2 

o'9 

358 

391.0 

27.8 

2-55 
18 

72 
0.50 

9-15 

41.0 
30.1 
28.5 

0.9 

394 
406.8 

25-1 
2.42 

21 

72 

0.58 

9.46 

41.2 
29.9 

28.3 

0.8 
392 
453-2 

27.1 
2.72 
*7 

Cut  off    '     

Initial  pressure  in  the  cylinder  per 
square  inch   absolute  

Barometer,  inches  of  mercury  
Vacuum,  inches  of  mercury  
Back-pressure,  pounds  per  square 
inch,  absolute  
Temp,  of  superheated  steam   
Horse-power  
Steam  per  horse-power  per  hour, 

Combustible  per  horse-power  per 
hour,  pounds  ... 
Per  cent  of  water  in  cylinder  at 

There  is  a  very  considerable  reduction  of  the  water  in  the 
cylinder  at  release,  which  explains  sufficiently  the  reason  for 
this  notable  gain  in  economy. 

Dixwell's  Tests. — A  small  Harris-Corliss  engine  was 
fitted  up  for  making  tests  on  superheated  steam  at  the 
Massachusetts  Institute  of  Technology  by  Mr.  George  B. 
Dixwell.  Six  tests  with  superheated  and  saturated  steam 
were  made  on  this  engine  in  1877  m  the  presence  of  a  board 


ECONOMY   OF  STEAM-ENGINES. 


371 


of  United  States  naval  engineers.  The  steam  was  generated 
in  cylindrical  tubular  boilers  and  was  superheated  in  a  vertical 
boiler  with  a  detached  brick  furnace.  Three  different  points 
of  cut-off  were  tried  for  each  condition  of  steam ;  the  cut-off 
was  controlled  by  the  governor  in  the  usual  way  when  the 
cut-off  was  less  than  half  stroke;  when  it  was  more  than  half 
stroke  the  valve  was  not  released  by  the  drop  cut-off 
mechanism  and  the  cut-off  was  produced  by  the  lap  of  the 
valve  as  for  a  plain  slide-valve. 

TABLE  XXVII. 

DIXWELL'S   TESTS   ON    SUPERHEATED    STEAM. 

CYLINDER   DIAMETER    8    INCHES;    STROKE    2    FEET. 

Proceedings  of  the  Society  of  Arts,  Mass.  Inst.   Tech.,  1887-88. 


Saturated  steam. 

Superheated  steam. 

I 

II 

III 

IV 

V 

VI 

127 
0.217 
61.5 

50.4 
J5-4 

302 
278-297 

52.2 

3*-4 
7.05 
48.2 
796 

83 
o-443 
60.4 

50.2 
»5-7 

3°3 

279-296 

35-9 
29.3 
12.7 
42.2 
696 

63 
0.689 
58.0 

50-3 
15.8 

303 
282-300 

27.9 
23-9 
15.68 
45-3 
747 

180 
0.218 
61.0 

50.4 
15-2 

478 
3i3 

27.4 
18.3 
6.83 

»•* 

631 

108 
0.439 
61.4 

50.0 
iS-4 

441 
3i6 

13-6 
13-6 
12.37 

& 

75 
0.672 

59-5 

50.2 
»5-5 

406 
315 

8.9 
"•5 
15-63 
35-8 
621 

Boiler-pressure  above  atmosphere,  pounds 

Back-pressure,  absolute,  pounds  per  sq  in. 
Temperatures  Fahrenheit: 

Per  cent  of  water  in  cylinder: 

Steam  per  horse-power  per  hour,  pounds.. 
B.  T.  U.  per  horse-  power  per  minute.  .  .  . 

A  metallic  thermometer  or  pyrometer  was  placed  in  a 
recess  in  the  head  of  the  cylinder.  When  saturated  steam 
was  used  this  pyrometer  showed  a  large  fluctuation,  but  when 
superheated  steam  was  used  its  needle  or  indicator  was  at  rest. 
Even  if  a  part  of  the  apparent  change  of  temperature  with  satu- 
rated steam  is  attributed  to  the  vibration  of  the  needle  and 
the  multiplying  mechanism,  it  is  very  clear  that  the  use  of 
superheated  steam  reduces  the  change  of  temperature  of  the 
cylinder-head  in  a  remarkable  manner.  The  effect  of  super- 


372  THE R MOD  YNAMICS   OF   THE   STEAM-ENGINE. 

heating  on  the  action  of  the  cylinder-walls  is  also  indicated 
by  the  per  cent  of  water  in  the  cylinder  at  cut-off  and  release. 
The  apparent  gain  by  comparing  the  amounts  of  steam 
used  per  horse-power  per  hour  in  favor  of  superheated  steam 
is 

42.2  -  31.7 


42.2 


X  ioo  =25  per  cent; 


but  this  result  is  of  course  illusive,  since  the  superheating 
required  additional  coal.  As  the  coal-consumption  was  not 
determined,  we  must  compare  instead  the  B.  T.  U.  per  horse- 
power per  minute,  giving  a  real  gain  of 

696  —  546 

X  I0°  =  I 


Superheated  Steam  in  Triple  Engines.  —  Recent  tests 
have  been  made  in  Germany  on  compound  and  triple-expan- 
sion engines  using  superheated  steam  with  extraordinary 
results.  In  Table  XXVIII  are  given  the  results  of  tests  on 
a  triple-expansion  engine  at  Augsburg.  This  engine  has  four 
cylinders,  a  high-pressure,  an  intermediate,  and  two  low- 
pressure  cylinders.  The  high-pressure  cylinder  and  one  low- 
pressure  cylinder  are  in  line  on  one  side  of  the  fly-wheel,  and 
the  intermediate  cylinder  and  the  other  low-pressure  cylinder 
are  in  line  on  the  other  side.  The  two  cranks  are  at  right 
angles.  Each  cylinder  is  jacketed  with  steam  on  the  barrel 
only  and  has  four  double-acting  poppet-valves.  The  cylin- 
ders are  cast  with  double  walls,  so  that  there  is  no  chance  for 
undetected  leakage  from  the  jackets. 

The  steam  is  superheated  in  a  coil  beyond  the  boiler,  and 
the  gases  afterwards  pass  through  a  feed-water  heater  or 
economizer,  by  which  they  are  reduced  to  a  comparatively 
low  temperature.  The  coal  used  appears  to  have  been  of 
poor  quality,  so  that  while  the  steam-  and  heat-consumptions 
are  good  the  coal  used  per  horse-power  per  hour  is  large  for 
such  an  engine.  Comparing  the  best  steam-consumption  for 


ECONOMY  OF  STEAM-ENGINES. 


373 


superheated  and  for  saturated  steam,   the  gain  from   super- 
heating appears  to  be 


13-2  —  12 
13.2 


X  100  =  9  per  cent. 


The  real  gain,  found  from  a  comparison  of  the  thermal  units 
per  horse-power  per  minute,  is 

235  -  228 


235 


X   100  =  3  per  cent. 


TABLE   XXVIII. 

TRIPLE-EXPANSION    HORIZONTAL    MILL-ENGINE    AT   AUGS- 
BURG WITH    SUPERHEATED    STEAM. 

CYLINDER     DIAMETERS     27.56,    43.31,    AND     TWO     OF     59.06     INCHES  ;      STROKE 

63    INCHES. 

By  Professor  M.  SCHROTER,  Zeitschrift  des    Vereines  Deutscher  Ingenieure, 

vol.  xl,  p.  249. 


Superheated. 

Saturated. 

1 

II 

III 

IV 

V 

VI 

1191 
416 
60.23 
39-9 
13-6 

89.7 
13-9 

2.O 
6.28 

433 
330.1 
414.7 

1167 
419 
60.  10 
39-4 
13-1 

89.4 

13.8 

1.9 
5.18 

441 

329-9 
418.1 

1028 
415 
60.24 
32.7 
16.2 

89.2 

13.8 

1-7 

7.28 

448 
329-7 
420.1 

12OI 
406 
60.47 
38.6 
14.4 

90.7 
13-8 

1.9 
9.18 

977 
416 
60.02 
28.6 
18.9 

89.4 
13.8 

i-7 

10.57 

993 
420 
60.05 
28.0 
19-3 

88.9 
13.8 

1.6 
12.40 

Duration    minutes  

Revolutions  per  minute  
Cut-off  high-pressure  cylinder.  .  .  . 

Steam-pressure   at   boiler,  pounds 
per  sq.  in.  above  atmosphere.  .  . 
Barometer,  pounds  per  sq.  in  
Back-pressure,    absolute,    pounds 
per  sq    in  

Condensation  in  jackets,  per  cent 

Temperatures  Fahrenheit: 
At  boiler,  superheated  

*  '        "        saturated  

330.8 

329-9 

329.5 

At  engine,  superheated  

325.7 

326.8 

327.6 

Hot  gases  before  economizer. 
"        after  economizer  .. 
Steam   per  horse-power  per  hour, 

498 
288 

13-0 
3-03 

4.49 
2.44 

527 
316 

12.7 
3.08 

4.29 
337 

5i6 
300 

12.0 

2.85 

4.41 
2.28 

14-3 

3-56 

3.96 
2-54 

13-5 
3-65 

4.00 
2.41 

13-2 
3-39 

3-86 
2.35 

Coal    per    horse-power    per    hour, 
pounds     .  .        

Pounds   of  water  evaporated    per 
pound  of  coal  from  and  at  212°  F. 
B.  T.  U.  per  horse-power  per  min. 

374          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  coal  used  is  of  such  inferior  quality,  and  the  con- 
sumption  per  horse-power  per  hour  is  so  irregular  that  it 
cannot  be  used  as  a  useful  basis  of  comparison. 

Schmidt's  System. — Table  XXIX  gives  a  resume  of  tests 
on  various  steam-engines  using  superheated  steam  according 
to  a  system  devised  by  Wilhelm  Schmidt.  His  system 
consists  in  part  in  the  arrangement  of  the  boiler  for  generat- 
ing the  steam  and  in  part  in  the  construction  of  the  engine. 
The  engine  and  boiler  on  which  the  tests  I  to  IV  were  made 
may  be  taken  as  a  type  of  the  system. 

The  boiler  is  vertical,  ten  feet  six  inches  high  and  five  feet 
six  inches  in  diameter.  It  has  a  corrugated  fire-box  and 
combustion-chamber  about  seven  feet  six  inches  high,  from 
which  the  products  of  combustion  pass  through  a  flue  22 
inches  in  diameter  to  the  superheater.  The  upper  part  of  the 
furnace  or  combustion-chamber  is  crossed  by  two  circulation- 
tubes,  each  about  16  inches  in  diameter.  The  fire-box  just 
above  the  grate  and  the  flue  at  the  top  of  the  combustion- 
chamber  are  lined  with  fire-brick.  The  superheater  is  a 
continuous  coil  of  pipe,  2.4  inches  in  diameter,  arranged  in 
twelve  flat  coils  with  five  turns  in  each.  Above  the  super- 
heater is  a  feed-water  heater,  which  is  also  a  continuous  coil 
of  pipe,  the  diameter  being  1.5  of  an  inch;  it  has  four  flat 
coils  of  five  turns  each.  The  central  space  inside  the  coils  of 
the  superheater  and  feed-water  heater  is  occupied  by  a  closed 
cast-iron  tube  22  inches  in  diameter.  This  arrangement  of 
boiler  superheater  and  feed-water  heater  permits  of  a  high 
degree  of  superheating  together  with  a  fair  evaporative 
efficiency,  as  the  gases  from  the  superheater  are  cooled  to 
about  400°  F.  by  the  feed- water  heater.  The  superheater, 
like  all  coil  superheaters,  is  subject  to  rapid  wasting,  for  the 
temperature  of  the  steam  inside  is  about  600°  F.,  while  the 
gases  outside  are  about  1200°  F.  In  this  case  two  such 
boilers  are  used  to  supply  an  engine  which  develops  one 
hundred  horse-power. 

The  engine  has  two  single-acting  horizontal  high-pressure 


ECONOMY   OF  STEAM-ENGINES. 


375 


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TEST 
Recorded  by  Profess 

ters  of  cylinders,  inches  . 
,  inches  

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re  of  steam,  pounds  per  s 
ratures:  saturated  steam, 
superheated  stea 
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3?  THERMODYNAMICS   OF    THE    STEAM-ENGINE. 

cylinders  and  one  double-acting  vertical  low-pressure  cylinder. 
The  high-pressure  cylinders  have  a  special  form  of  piston- valve 
controlled  by  a  shaft-governor;  the  low-pressure  cylinder  has 
a  double-ported  slide-valve.  The  low-pressure  cylinder  has 
a  steam-jacket,  and  arrangements  are  made  for  superheating 
the  steam  between  the  high-pressure  and  the  low-pressure 
cylinders. 

Of  the  tests  I  to  IV  oade  on  this  engine  the  first 
was  made  without  superheating  of  the  steam  between  the 
two  cylinders;  during  the  second  test  the  steam  was  again 
superheated  about  100°  F.  above  the  corresponding  tem- 
perature for  saturated  steam.  The  two  tests  III  and  IV  were 
made  at  a  reduced  boiler-pressure.  The  third  test  was  made 
with  and  the  second  without  steam  in  the  jacket  of  the  low- 
pressure  cylinder. 

The  report  of  the  test  does  not  give  the  data  required  for 
calculating  the  heat-consumption,  so  it  is  necessary  to  depend 
on  the  coal-consumption  per  horse-power  per  hour  in  making 
comparisons  with  other  engines,  since  in  this  case  the  steam- 
consumption  is  not  a  reliable  guide.  The  coal-consumption 
is  very  satisfactory,  but  is  not  exceptional. 

The  results  of  the  tests  VI  and  VII  made  by  Professor 
Schroter  on  a  comparatively  small  vertical  Schmidt  engine 
are  exceptional  in  both  the  steam  and  coal  economy;  the 
latter,  which  is  the  only  trustworthy  basis  of  comparison,  is  as 
small  as  the  best  result  given  in  Table  X  for  the  Leavitt 
pumping-engine  at  the  Chestnut  Hill  station,  Boston.  A 
further  comparison  oi  the  two  engines  shows  that  the  Schmidt 
engine  worked  with  less  steam-pressure  and  fewer  expansions. 
The  Leavitt  engine  had  21  expansions  while  the  Schmidt 
engine  had  16  expansions  in  test  VI  and  19  in  test  VII ;  these 
last  figures  are  not  given  in  Table  XXIX,  but  are  given  by 
Professor  Schroter  in  his  report. 

The  engine  tested  by  Professor  Schroter  was  a  vertical 
single-acting  tandem  compound  engine,  with  the  small  cylin- 
der over  the  large  cylinder.  The  high-pressure  piston  was  a 


ECONOMY   OF  STEAM-ENGINES.  377 

hollow  plunger  long  enough  to  carry  the  low-pressure  piston 
at  its  lower  end.  The  low-pressure  piston  had  for  its  effec- 
tive area  the  annular  ring  outside  the  plunger.  The  lower 
end  of  the  large  cylinder  was  closed  and  the  space  under 
the  large  piston,  including  the  space  in  the  hollow  plunger, 
formed  an  intermediate  receiver  with  variable  volume.  The 
high-pressure  cylinder  had  a  piston-valve,  and  the  low- 
pressure  cylinder  had  a  slide-valve,  cored  through  the  body 
to  give  a  double  admission  after  the  manner  of  the  Trick 
valve.  Both  valves  were  on  one  spindle  and  were  actuated 
by  a  single  eccentric.  The  boiler  was  of  the  type  already 
described. 

One  other  test  in  Table  XXIX  is  worthy  of  note,  that  is, 
test  V  on  a  compound  condensing-engine  which  developed  69 
horse-power  for  1.52  of  a  pound  of  coal  per  horse-power  per 
hour.  This,  though  less  remarkable  than  the  economy  for 
either  test  VI  or  test  VII,  is  exceptionally  good  for  an  engine 
of  that  size.  Other  tests  of  less  importance  are  recorded  in 
the  same  table  on  a  vertical  high-speed  non-condensing  engine 
and  on  two  horizontal  single-cylinder  engines.  The  vertical 
engine  was  tested  with  saturated  and  with  superheated  steam, 
and  would  appear  to  show  an  enormous  gain  from  super- 
heating; but  its  performance  with  saturated  steam  is  too  poor 
to  serve  as  a  basis  of  comparison. 

With  the  exception  of  tests  V,  VI,  and  VII  the  per- 
formance of  any  engine  recorded  in  Table  XXIX  may  be 
equalled  by  an  engine  of  the  same  power  using  saturated 
steam  if  we  take  for  the  basis  of  comparison  the  coal  con- 
sumed per  horse-power  per  hour.  The  exceptionally  small 
steam-consumptions  shown  by  some  tests  appear  to  be  mis- 
leading. 

Steam-jackets. — A  comparison  of  the  results  of  applica- 
tions of  Hirn's  analysis  to  engines  with  and  without  steam- 
jackets  leads  to  the  conclusion  that  the  beneficial  effect  of  a 
steam-jacket  is  indirect.  It  appears  that  while  some  heat  is 
supplied  by  the  jacket  during  expansion  (a  part  of  which  may 


378  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

be  changed  into  work)  the  greater  part  is  supplied  during 
exhaust  and  is  carried  away  by  the  exhaust  steam  and  lost. 
But  the  indirect  effect  is  to  maintain  the  inner  wall  of  the 
cylinder  at  a  higher  temperature,  and  so  reduce  the  initial 
condensation,  and  consequently  to  reduce  the  exhaust-waste. 
It  further  appears  that  the  exhaust-waste  is  not  a  proper 
criterion  of  the  economy  of  the  engine,  and  that  while  a 
lavish  use  of  steam-jackets  on  compound  engines  may  extin- 
guish the  exhaust-waste  we  cannot  expect  to  get  the  highest 
economy  by  that  process. 

It  is  not  possible  from  any  theoretical  discussion  nor  from 
a  study  of  all  the  applications  of  Hirn's  analysis  now  extant 
to  determine  when  or  to  what  extent  steam-jackets  are  advan- 
tageous. We  must,  consequently,  go  direcfly  to  comparative 
tests  of  engines  with  and  without  steam-jackets.  Properly 
we  should  compare  engines  which  otherwise  are  identical  and 
which  differ  only  in  that  one  is  made  with  and  the  other 
without  a  steam-jacket.  Few  if  any  such  comparisons  can  be 
made;  in  general,  we  must  be  content  to  compare  tests  made 
on  an  engine  with  steam-jackets,  some  of  the  tests  being 
made  with  steam  supplied  to  the  jackets  and  some  without. 
This  method  of  comparison  is  not  quite  fair,  for  it  is  probable 
that  the  engine  which  has  a  steam-jacket  wastes  more  heat  by 
radiation  and  conduction,  both  when  there  is  and  when  there 
is  not  steam  in  the  jacket,  than  does  an  unjacketed  engine  of 
the  same  size  and  power.  However,  if  this  were  our  only 
difficulty  we  should  be  fortunate,  because  the  total  radiation 
is  in  no  case  large  for  a  properly  lagged  cylinder. 

A  haphazard  comparison  of  the  numerous  tests  that  have 
been  made  of  engines  with  and  without  steam  in  the  jackets 
may  be  made  to  show  anything,  from  a  most  extravagant  and 
improbable  gain  to  a  positive  loss.  It  is  proper,  by  the  way, 
to  say  that  when  a  jacket  shows  no  gain  the  engine  is  prob- 
ably better  and  is  certainly  cheaper  without.  In  order  to 
arrive  at  any  conclusion  it  is  necessary  to  proceed  according 
to  a  logical  system. 


ECONOMY   OF  STEAM-ENGINES.  3/9 

In  general,  nothing  can  be  learned  from  the  comparison 
of  individual  tests  either  on  a  given  engine  with  and  without 
steam  in  the  jackets  or  on  separate  engines.  Either  or  both 
of  the  tests  may  be  made  under  conditions  which  give  a  poor 
economy,  whereas  useful  comparisons  can  be  made  only 
when  conditions  are  favorable.  This  does  not  preclude  a 
comparison  when  both  tests  give  high  economy. 

When  possible,  tests  should  be  in  series,  extensive  enough 
to  determine  the  conditions  which  give  the  best  economy 
both  with  and  without  jackets;  and  in  such  case  only  the  best 
results  for  each  condition  should  be  compared.  The  compari- 
son is  much  aided  by  drawing  curves  like  those  in  Fig.  81, 
page  390. 

A  few  tests  (eight  or  ten)  may  completely  determine  the 
interesting  part  of  the  curve,  as,  for  example,  the  lowest 
curve  on  Fig.  81.  In  this  case  there  are  virtually  four  pairs 
of  points  and  one  more  individual  point  which  definitely 
locate  the  curve.  The  three  detached  points  below  the  curve 
are  for  tests  which  differ  in  a  minor  particular. 

In  all  cases  the  comparison  should  be  of  the  heat-con- 
sumption instead  of  the  steam-consumption;  for  the  hot  water 
from  the  jackets  can  and  should  be  returned  to  the  boiler  at 
nearly  the  temperature  in  the  boiler,  or  else  should  be  used 
to  heat  the  feed-water  in  such  a  way  that  its  heat  is  not 
wasted. 

Though  such  a  method  will  simplify  our  investigations  and 
in  general  lead  to  consistent  results,  we  will  find  some  dis- 
crepancies which  cannot  be  reconciled,  and  which  will  show 
why  there  is  so  much  difference  of  opinion  concerning  the 
advantage  to  be  obtained  from  the  use  of  steam-jackets. 

Delafond's  Tests. — In  1883  an  extensive  and  important 
investigation  was  made  by  Mons.  F.  Delafond  on  a  horizontal 
Corliss  engine  at  Creusot  to  determine  the  conditions  under 
which  the  best  economy  can  be  obtained  for  such  an  engine. 
The  engine  had  a  steam-jacket  on  the  barrel,  but  was  not 
jacketed  on  the  ends.  Steam  was  supplied  to  the  jacket  by 


THERMODYNAMICS   OF    THE   STEAM-ENGINE. 

a  branch  from  the  main  steam-pipe,  and  the  condensed  water 
was  drained  through  a  steam-trap  into  a  can,  so  that  the 
amount  of  steam  used  in  the  jacket  could  be  determined. 
The  engine  was  tested  with  and  without  steam  in  the  jacket, 
both  condensing  and  non-condensing,  and  at  various  pressures 
from  35  to  100  pounds  above  the  pressure  of  the  atmosphere. 
The  effective  power  and  the  friction  of  the  engine  were  also 
obtained  by  aid  of  a  friction-brake  on  the  engine-shaft. 

The  piping  for  the  engine  was  so  arranged  that  steam 
could  be  drawn  either  from  a  general  main  steam-pipe  or 
from  a  special  boiler  used  only  during  the  test.  Before 
making  a  test  the  engine,  which  had  been  running  for  a 
sufficient  time  to  come  to  a  condition  of  thermal  equilibrium, 
was  supplied  with  steam  from  the  general  supply.  At  the 
instant  for  beginning  the  test  the  general  supply  was  shut  off 
and  steam  was  taken  from  the  special  boiler  during  and  until 
the  end  of  the  test,  and  then  the  pipe  from  that  boiler  was 
closed.  The  advantage  of  this  method  was  that  at  the 
beginning  and  end  of  the  test  the  water  in  the  boiler  was 
quiescent  and  its  level  could  be  accurately  determined.  At 
the  end  of  a  test  the  water-level  was  brought  to  the  height 
noted  at  the  beginning.  The  water  required  for  feeding 
the  special  boiler  during  the  test  and  for  adjusting  the 
water-level  at  the  end  was  measured  in  a  calibrated  tank. 
As  the  steam-pressure  in  the  general-supply  main  and  in  the 
special  boiler  was  the  same,  there  was  little  danger  of  leakage 
through  the  valves  for  controlling  the  steam-supply;  the 
regularity  and  consistency  of  results  shown  by  the  curves  of 
Figs.  79  and  80  attest  to  the  skill  and  accuracy  with  which 
these  tests  were  made. 

Table  XXX  gives  the  results  of  tests  made  with  conden- 
sation, and  Table  XXXI  gives  the  results  of  tests  without 
condensation.  All  the  tests  both  with  and  without  conden- 
sation, but  during  which  no  steam  was  used  in  the  jackets,  are 
represented  by  the  several  curves  of  Fig.  79,  while  Fig.  80 
represents  tests  made  with  steam  in  the  jackets.  The  curves 


ECONOMY   OF  STEAM-ENGINES.        %  381 

TABLE    XXX. 

HORIZONTAL   CORLISS    ENGINE    AT   CREUSOT. 

CYLINDER    DIAMETER  21. 65    INCHES  J    STROKE  43.3!    INCHES  J    JACKET   ON 
BARREL    ONLY  ;    CONDENSING. 

By  F.   DELAFOND,  Annales  du  Mines,  1884. 


Number  of  test. 

Duration, 
minutes. 

Revolutions  per 
minute. 

Cut-off  in  per 
cent  of  stroke. 

Steam-pressure, 
pounds  per  sq. 
in. 

Vacuum,  inches 
of  mercury. 

Steam  used  in 
jacket,  per  cent. 

Indicated  horse- 
power. 

Steam  per  horse- 
power per  hour, 
pounds. 

i 

60 

60.0 
-8  6 

j 

96.3 

qg  g 

27.1 



109 
128  ? 

23.2 

37  o 

161 

H 

1  86 

4 

1 

7 
8 

73 

g 

39 

58.8 
61.5 
59-9 
58-1 

£ 

6.7 
12.5 

104 

102.4 
103.8 
105.2 

27.4 
27.1 
27.4 

26.8 

? 
? 
2.9 
3-2 

Mi 
J59-5 
J55 

212 

17.1 
16,7 
16.5 
17.6 

-o  8 

79.8 

27.  1 

126 

10 

TOO 

59-3 

_0  g 

:i 

81.1 

go  ! 

27.4 



f34 

21  .1 

20  8 

eg  o 

85.5 

175 

'3 
14 

11 

17 

50 

94 

102 

4° 
4° 

59-i 
59-6 
59-6 

60.0 

Is 

5 
5-5 
11.5 
14 

sl! 

Bt? 

84.i 

26.5 

27.4 
27.6 
27.1 
27.0 

3-o 
3.i 

1.2 

x-5 

*94 

112 
124 
I76 

193 

20.4 

T7-7 

T3 
16.9 

*7.5 

18 

Ql 

eg  -, 

60.5 

28.0 

85  :» 

i9 

20 
21 

90 

75 

59-5 
59.0 

eg  J 

9 
iS-5 

55-8 
61.2 
58.3 

27.6 

.27.8 

27.6 



"5 

150 

172 

19.1 
18.1 
18.4 

61  2 

1  86 

18  8 

23 
24 
25 
26 
27 

"5 
92 
90 
71 
50 

59  9 
59  6 
58.8 
59-1 
59  -o 

2i 

9 
iS-5 

20 

25 

59-9 
59-9 
60.9 
61.9 
62.3 

27.8 

*7-4 
27.1 
26.8 
26.4 

2.5 
2.5 

1.8 

\\ 

91-7 
117 

150 
175 

IQ4 

18.5 
17.6 

'7-3 
17.7 
18.6 

28 

60  7 

6 

28.0 

7S  6 

29 

80 

58.8 

6O  A 

9-5 

48.9 

28.1 

27  6 



94.3 

19.4 

18  8 

3° 

in 

58  8 

47  8 

27  6 

476 

165 

19.8 

33 
34 

P 

37 

II 
£ 

74 
50 

*. 

57-6 
59-7 
60.  i 

59-5 

5 

10 

14-3 

22 

29 

45.8 
5i.6 
49.1 
48.6 
50.2 

28.0 
27.6 
28.1 
27.8 
26.8 

2  6 

2  3 
i  4 

*  4 

I  2 

Si 

95.5 

120 

152 
179 

J9-3 
18.5 
18.2 
18.9 
19.7 

18 

g- 

60  * 

18  2 

27  8 

106 

68 

61  i 

26  C. 

1  60 

567 

34-7 
•26  7 

26  o 

181 

182 

42 
43 

44 
45 

i 

40 
25 

60.7 
61.9 
61.1 
60.4 

»9 

SI 

100 

32.0 

33-o 
35-i 
34-7 

f. 

27.6 

26.5 

20.0 
25.2 

1.6 
I.I 

0.6 

0.2 

in 
162 

180 

199 

19.8 

22.  I 
25-4 

33-o 

.382 


THERMODYNAMICS    OF   THE   STEAM-ENGINE. 


TABLE   XXXI. 

HORIZONTAL   CORLISS    ENGINE    AT    CREUSOT. 


CYLINDER    DIAMETER   21.6$    INCHES  ;    STROKE  43-31   INCHES 
BARREL  ONLY;  NON-CONDENSING. 

By  F.  DELAFOND,  Annales  des  Mines,  1884. 


JACKET    ON 


V 

V. 

s 

ai 

1 

in 

•sS. 

u 

"o 

<u 

U 

Jl 

gj 

§1 

.2  c 

ga 
|i 

u  a 

ill 

Sow 

M  S 

III 

sis 

4  2  •) 

3*« 

sl 
ii 

y 

ipi 

H  C  h  P 

«  o  i>  o 
«j3  aa. 

z, 

Q 

ri 

u 

C/3 

w 

Cfl 

73 

6l   7 

T-J 

6 

28.4 

/  ° 

f  *•  / 

61.4 

*J 

1  7 

IOO.  2 

181.5 

26.8 

2C 

63.6 

A  y 

IO2  O 

217 

25.8 

4 

80 

60.8 

II 

98.1 

2.5 

•*  / 
143 

22.8 

5 

60 

62.O 

13 

103.8 

3-4 

177-5 

22.1 

6 

36 

62.0 

16 

103.0 

3.1 

194 

22.4 

7 

30 

62.7 

20 

103-5 

2.O 

237 

21-5 

8 

66 

62.0 

15-5 

73-7 



121 

27-6 

60 

60.9 

18 

77  O 

1-^6 

26  7 

IO 

60 

6O.O 

24    <\ 

//*** 

76  7 

A  j" 

178 

•v«  / 

24.6 

T  T 

6O.6 

•^4*  3 

yvj.  y 

77  ^ 

i  y  u 

24.  2 

12 

70 

61.1 

16.5 

/  /  *  j 
77.0 

1-7 

137 

23.7 

13 

50 

61.6 

23-5 

75.8 

1.2 

1  80 

21.8 

14 

30 

60.5 

30 

78.0 

1.3 

204 

22.0 

fSr    1 

50.8 

108 

27   1 

16 

70 

6i!i 

37 

51.2 



147 

^  /  •  j 
27.2 

17 

50 

60.9 

58 

50.5 



173 

30.2 

18 

25 

60.6 

IOO 

34-9 



145 

46.8 

19 

70 

60.5 

23 

52.6 

1-5 

108 

25-3 

20 

60 

60.5 

34 

51.8 

I.I 

141.5 

2^.2 

21 

50 

60.3 

58 

46.2 

0.7 

168.5 

28.7 

22 

30 

61.1 

IOO 

33-7 

0-3 

147-5 

46.3 

are  lettered  to  show  the  mean  steam -pressure  for  the  series 
represented  and  the  condition,  whether  with  or  without 
condensation.  Thus  on  Fig.  79  the  lowest  curve  6oC  repre- 
sents tests  made  without  steam  in  the  jackets  and  with  con- 
densation, while  the  highest  curve  on  Fig.  80  represents  tests 
without  steam  in  the  jackets  and  without  condensation,  at  50 
pounds  boiler-pressure.  The  abscissae  for  the  curves  are  the 
per  cents  of  cut-off  and  the  ordinates  are  the  steam-consump- 
tions in  pounds  per  horse-power  per  hour.  The  results  for 
individual  tests  are  represented  by  dots,  through  which  or  near 


ECONOMY  OF  STEAM-ENGINES. 


383 


which  the  curves  are  drawn.  As  there  are  only  a  few  tests  in 
a.ny  series,  a  fair  curve  representing  the  series  can  be  drawn 
through  all  the  points  in  most  cases.  The  exceptions  are 
tests  made  with  condensation  for  boiler-pressure  of  80  and 


30 


24 


20 


18 


10 


30  40 

FIG.  79- 


50 


100  pounds  per  square  inch.  The  forms  of  the  curves  SoC 
and  ioo£7,  Fig.  79,  were  made  to  correspond  in  a  general  way 
to  the  curves  506"  and  6oC.  The  discrepancies  appear  large 
on  account  of  the  large  scale  for  ordinates,  but  they  are  not 
really  of  much  importance;  the  largest  deviation  of  a  point 
from  the  curve  1006*  is  half  a  pound  out  of  about  22,  which 
amounts  to  little  more  than  two  per  cent.  On  Fig.  80  the 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


curve  SoC  is  drawn  through  the  points,  but  though  its  form 
does  not  differ  radically  from  the  .curves  6oC  and  50^,  so 
marked  a  minimum  at  so  early  a  cut-off  is  at  least  doubtful. 
Considering  that  the  probable  error  of  determining  power 


30 


24 


22 


18 


16 


\ 


10 


20  30 

FIG.   80. 


50 


from  the  indicator  is  about  two  per  cent,  it  would  not  be 
difficult  to  draw  an  acceptable  curve  in  place  of  SoC  which 
should  correspond  to  the  forms  of  6oC  and  $oC. 

The  results  of  the  four  tests  made  with  steam  in  the 
jacket  and  with  condensation,  and  which  are  numbered  5,  6, 
7,  and  8  in  Table  XXX,  are  represented  by  dots  inside  of 


ECONOMY   OF  STEAM-ENGINES.  385 

small  circles  on  Fig.  80.  It  does  not  appear  worth  while  to 
try  to  draw  a  curve  to  represent  these  tests. 

From  a  comparison  of  the  curves  on  Figs.  79  and  80  repre- 
senting the  results  of  tests  stated  in  Tables  XXX  and  XXXI, 
it  appears  that  the  engine  when  running  condensing,  whether 
with  or  without  steam  in  the  jackets,  gave  its  best  economy 
at  about  one-sixth  cut-off.  When  running  non-condensing 
the  cut-off  giving  the  best  economy  was  at  about  one-third 
stroke.  A  more  careful  consideration  of  the  proper  cut-off 
for  simple  engines  and  of  the  total  expansions  for  multiple- 
expansion  engines  will  be  given  later  and  then  somewhat  fine- 
discriminations  may  be  attempted.  The  general  statement 
given  above  will  suffice  for  our  present  purpose. 

It  has  already  been  pointed  out  that  these  tests  show  that 
the  best  results  are  obtained  from  this  engine  running  con- 
densing and  without  steam  in  the  jacket  for  a  boiler-pressure 
of  60  pounds.  With  steam  in  the  jacket  the  advisable  pres- 
sure is  at  least  80  pounds.  Taking  for  comparison  tests  16 
and  20  of  Table  XXX,  the  gain  from  the  use  of  the  jacket  is 

18.1  —  16.0 

—3—      -  X   ioo  =  7  per  cent. 

1  o.  1 

All  the  tests  with  steam  in  the  jacket  show  a  very  small 
percentage  condensed  in  the  jacket,  so  small  as  to  raise  the 
question  whether  the  steam-trap  for  removing  the  condensed 
water  could  have  acted  properly.  But  we  have  not  the  datai 
for  calculating  the  heat-consumption  in  any  case,  and  so  must 
rest  content  with  the  comparison  made. 

The  tests  made  on  the  engine  without  condensation  are 
less  complete,  and  on  the  whole  it  appears  best  to  compare 
only  the  tests  made  at  75  pounds  boiler-pressure.  Comparing, 
tests  ii  and  13,  Table  XXXI,  the  gain  from  the  use  of  the 
steam  in  the  jacket  is 


24.2  —  21.8 
24-2 


X  ioo  =  10  per  cent. 


.386  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

These  tests  by  Delafond  give  very  good  illustrations  of  the 
'error  and  confusion  that  may  arise  when  individual  tests  are 
compared  to  determine  the  advantage  to  be  obtained  from 
the  use  of  a  steam-jacket.  Thus  a  comparison  of  tests  2  and 
7  of  Table  XXX  shows  an  apparent  gain  in  steam-consump- 
tion of  25  per  cent,  while  a  comparison  of  tests  31  and  36 
.shows  a  slight  loss  from  the  use  of  steam  in  the  jacket. 
Both  pairs  of  tests  standing  by  themselves  would  appear  to 
•give  a  fair  basis  for  comparison;  it  is  only  by  assembling 
several  series  of  tests,  as  by  aid  of  the  curve  of  Figs.  79  and 
So,  that  the  real  value  of  the  steam-jacket  can  be  determined. 

Tests  on  Revenue  Steamers. — In  1874  three  steamers, 
the  Rush,  the  Dexter,  and  the  Dallas,  were  built  for  the 
United  States  revenue  marine,  which  were  designedly  alike 
in  all  respects  except  that  the  engines  were  of  three  distinct 
types,  and  the  boilers  were  adapted  to  the  engines.  This 
was  done  to  determine  which  type  was  best  adapted  to  the 
needs  of  the  service.  At  about  the  same  time  another 
steamer,  the  Gallatin,  was  supplied  with  a  new  engine  differing 
from  those  in  the  vessels  just  mentioned.  Again,  the 
Treasury  Department  had  a  small  steamer  built  in  1870  for  the 
use  of  the  Coast  Survey,  named  the  Bache.  These  five 
steamers  had  their  engines  tested  under  the  direction  of  Chief 
Engineer  C.  H.  Loring,  U.S.N.,  and  Mr.  Chas.  E.  Emery, 
Consulting  Engineer  U.  S.  R.  M.  During  the  tests  the 
vessels  were  secured  to  the  dock.  One  test  on  each  engine 
was  long  enough  to  determine  the  coal-consumption;  other 
tests  were  shorter  and  for  them  the  steam-consumption  only 
was  determined.  The  feed-water  was  measured  in  a  tank  with 
two  compartments,  which  were  filled  and  emptied  alternately, 
and  was  used  as  the  basis  for  determining  the  steam-con- 
sumption. 

The  Rush  had  a  compound  engine  with  the  pistons  con- 
nected to  cranks  at  right  angles.  The  cylinders  were  jacketed 
on  barrels  and  heads.  The  small  cylinder  had  a  separate 
.cat-off  valve  on  the  back  of  the  main  valve. 


ECONOMY  OF  STEAM-ENGINES. 


387 


The  Bache  had  a  compound  engine  with  both  pistons  on 
one  continuous  piston-rod,  the  high-pressure  cylinder  being 
over  the  low-pressure  cylinder.  The  large  cylinder  only  had 
a  steam-jacket  on  barrel  and  ends.  The  engine  was  piped  to 
run  compound  or  single,  using  the  low-pressure  cylinder  only 
in  the  latter  condition. 

The  Dexter  had. a  single-cylinder  engine  without  steam- 
jackets,  and  the  Dallas  had  an  engine  of  the  same  type,  but 
intended  for  a  lower  steam-pressure. 

The  Gallatin  had  a  single-cylinder  engine  jacketed  on  the 
barrel  and  heads.  During  tests  on  this  engine  the  steam- 
consumption  was  determined  by  collecting  and  weighing  the 
water  drawn  from  the  condenser. 

The  results  of  the  tests  on  these  several  engines  are  given 
in  Table  XXXII.  The  best  results,  together  with  the  thermal 
units  per  horse-power  per  minute,  are  assembled  in  the  fol- 
lowing supplemental  table: 


No.  of 
test. 

Name  of 
engine. 

Method  of  working. 

Boiler-pressure, 
gauge. 

Back-pressure, 
absolute. 

Revolutions 
per  minute. 

Total  number 
of  expansions. 

Indicated 
horse-power. 

Steam  per 
horse-power 
per  hour. 

Thermal  units 
per  horse- 
power per  min. 

6 

2 

18 

Bache  
Rush.  

Compound  with  jacket... 
without    ' 

80.2 
80.3 

3-3 
3-4 

53-2 
47-7 

7-° 
6-7 

99.2 
69.8 

266  5 

20.3 
23.0 

3f>l 
408 

16 
13 

22 

Bache  
Dexter  

Simple  with  jacket   .  .     . 
'    without    "      ... 

79-5 
78.1 
68  7 

3-7 
4.4 

S3-8 

47-i 

t-6  c 

5-i 
5-3 

1  16.0 
89.2 

23.2 

26  2 

411 
460 

36 

34 

Gallatin  

"      with         "      ..     . 
'    without     "       ..     . 

S.J 

68.5 

3-6 

3-9 

i«-s 
71.6 

59-9 

3-6 
4-9 

179  •? 
279.  f 

20.5 
21.9 

423 

361 
387 

For  the  present  we  will  consider  only  those  tests  which 
may  be  used  to  determine  the  advantage  of  using  steam- 
jackets;  the  effects  of  using  higher  pressures  and  of  com- 
pounding will  be  considered  later. 

Comparing  tests  34  and  36  on  the  Gallatin  with  and  with- 
out steam  in  the  jacket  shows  a  gain  in  steam-consumption 
from  the  use  of  the  jacket  of 
21.9  —  20.5 


21.9 


X  ioo  =  7  per  cent. 


388 


THERMOD  YNA  Ml  CZ    OF   THE  '  S  TEA  M-ENGINE. 


TABLE   XXXII. 

TESTS    ON    THE   U.    S.    REVENUE  STEAMERS  RUSH,   DEXTER, 

DALLAS,      AND     GALLATIN,  AND      THE      COAST-SURVEY 
STEAMER  BACHE. 

Bache.  Ru±h.           Dexter.      Dallas.     Gallatin. 

Cylinder  diameters;inches...  16  &  25  24  &  28    26     36    34.1 

Stroke,  inches 24  27       36     30     30 


g 

u 

a 

§ 

gj 

£ 

. 

C 

| 

%$ 

0    ° 

3 

»r  J3 

•5  x 

2f  -Q 

OT3 

U            1 

2^3 

S 

6 

S 

9 

Condition. 

Duration,  h< 

Revolutions 
minute. 

Total  expan 

8«c 

u  or~ 

9-  3? 

u  bo"5 

F 

Barometer, 
pounds  pe 
square  inc 

Vacuum,  in 
of  mercur 

P* 

Percentage 
steam  use 
jackets. 

\      I 

8. 

X 

Steam  per  I 
power  per 
pounds. 

Comp. 

1.83 

42.6 

9.i 

82.0 

14.7 

24.0 

3-4 

55-9 

23.8 

2 

without 

2.07 

47>7 

6.7 

80.  , 

14.7 

24-3 

3-4 



77.1 

23.0 

3 

jacket. 

2.13 

49-3 

5-6 

80.3 

14.7 

24.7 

3-3 

85-8 

23-2 

4 

J.73 

38.9 

16.9 

81.  4 

14.9 

^4-5 

3-7 

6-5 

46.4 

25-1 

5 

2.07 

48.2 

9.2 

80.3 

14.9 

26.5 

7.0 

77-5 

20.7 

6 
7 

Comp. 
with 

I  '.98 

53-2 
56.3 

7.0 
5-7 

80.2 

80.  T 

14.9 
14.9 

26.5 
26.6 

3-3 
3-3 

S3' 

99.2 
1  10.  6 

20.3 
20.4 

8 

jacket. 

7.07 

55-6 

5-7 

8o.O 

26.1 

3-4 

106.0 

22.0 

9 

10 

Bache. 

15.23 

2.00 

S3-  0 
60.6 

4.2 

79-» 

79-1 

14-3 
14.9 

31 

3-3 
3-3 

4.0 

102.3 
134-5 

22.4 
21.2 

ii 

Single 

.80 

37-3 

ii.  8 

81.0 

14.6 

24.0 

4.6 

47.2 

35-° 

12 

without 

.98 

44.9 

7-6 

79.6 

14.6 

23.8 

4-4 

71.8 

29.6 

*3 

jacket. 

47.1 

5-3 

78.1 

14.6 

24.2 

4-4 

89.1 

26.2 

H 

Single 
with 
jacket. 

.10 

.68 

.12 

.88 

39-9 
46.2 
53-8 
45-3 

12.6 

8.6 

2    2 

80.8 
81.1 
79.6 

30-9 

14.6 
14.6 

.4.6 
14.6 

24-7 
25-3 
25-5 
24.0 

3-0 

2.8 

3.7 

4-7 

4.0 
1.8 

2.2 

54-8 
74-6 
116.0 
66.7 

27.1 
24.1 
23.2 
34>o 

8 
9 

Rush. 

Comp. 

with  jacket. 

5I 

70.8 
55-5 

6.2 
4.0 

69.1 
36.7 

14-8 
14.8 

26.5 
26.2 

3-5 
3-4 

P 

266.5 
168.7 

18.4 

22.1 

20 

2.92 

56.5 

4-5 

68.7 

14.8 

25-9 

3-4 

186.9 

23-9 

21 

1.42 

64.3 

3-7 

69.3 

14.8 

25.2 

3-7 



228.1 

24.1 

22 

Single 

34-5 

61.1 

3-5 

67.1 

14.8 

25-5 

3«6 

2T9.0 

23-9 

23 

Dexter. 

without 

72.8 

2.7 

66.4 

14.8 

25-3 

5-3 

292.4 

24-3 

24 

jacket. 

1.32 

50.8 

3-3 

40.6 

14.8 

26.1 



28.8 

25 

1.20 

55-3 

2-4 

39-9 

14.8 

26.0 

3-6 

161.8 

28.9 

26 

0.92 

60.7 

2.  1 

41.9 

14.8 

25-5 

4-3 



196.2 

31-8 

27 

1.52 

48.7 

5-i 

35-4 

14.8 

26.1 

3-o 

138.0 

26.7 

28 

Single 

*-55 

56-9 

3-4 

35-3 

14.8 

26.0 

3-4 

186.8 

26.9 

29 

Dallas. 

without 

31.0 

61.5 

3-1 

32.0 

14.7 

25.2 

3-9 



221  .4 

26.9 

3° 

jacket. 

i.  60 

64-5 

2.9 

33-7 

14.8 

25-4 

242.8 

28.9 

31 

i-53 

63-5 

2-3 

27.4 

14.8 

24.8 

4.1 



234-3 

31.0 

33 

Single 

24.0 

60.3 

4-5 

64.1 

14.9 

25-3 

43 

247.9 

24-3 

33 

without 

2.05 

56.0 

5-6 

68.2 

14.6 

25-1 

4-7 



212.2 

23-8 

34 

, 

jacket. 

2.02 

59-9 

4-9 

68.5 

14.8 

25-9 

3-9 

259.0 

21.9 

35 

Single 
with 

24.0 
2.22 

61.5 

S1'! 

4-5 
7-3 

65.4 
71.6 

14  7 
14-8 

25.1 
25-7 

4-° 

3-6 

3-5 
5-1 

260.5 

22.0 
20.5 

37 

jacket. 

1-93 

68.7 

4.2 

67.2 

14.8 

25.0 

4-4 

3-2 

324.4 

21-5 

ECONOMY   OF  STEAM-ENGINES.  389 

A  comparison  of  tests  13  and  16  on  the  Bache,  using  the  large 
Cylinder  only,  shows  a  gain  of 

26.2  —  23.2 

-~—      -  X  ioo  =  ii  per  cent. 
26.2 

Finally,  a  comparison  of  tests  2  and  6  on  the  Bache  as  a  com- 
pound engine  shows  a  gain  of 

23.0  —  20.3 

X   ioo  =  1 1  per  cent 
23.0 

from  jacketing  the  low-pressure  cylinder  only.  Comparisons 
based  on  thermal  units  per  horse-power  per  minute  give  the 
same  results,  because  the  per  cent  of  steam  used  in  the 
jackets  is  not  large  in  any  case. 

Experimental  Engine  at  the  Massachusetts  Institute 
of  Technology. — This  engine,  which  was  added  to  the  equip- 
ment of  the  laboratory  of  steam-engineering  of  the  Institute 
in  1890,  is  specially  arranged  for  giving  instruction  in  making 
engine-tests.  It  has  three  horizontal  cylinders  and  two 
intermediate  receivers,  the  piping  being  sp  arranged  that  any 
cylinder  may  be  used  singly  or  may  be  combined  with  one  or 
both  of  the  other  cylinders  to  form  a  compound  or  a  triple 
engine.  Each  cylinder  has  steam-jackets  on  the  barrel  and 
the  heads,  and  steam  may  be  supplied  to  any  or  all  of  these 
jackets  at  will.  The  steam  condensed  in  the  jackets  of  any 
one  of  the  cylinders  is  collected  under  pressure  in  a  closed 
receptacle  and  measured.  Originally  the  receivers  were  also 
provided  with  steam-jackets;  now  they  are  provided  with 
tubular  reheaters  so  divided  that  one-third,  two-thirds,  or  all 
the  surface  of  the  reheaters  can  be  used.  The  steam  con- 
densed in  the  reheaters  is  also  collected  and  measured  in  a 
closed  receptacle. 

The  valve-gear  is  of  the  Corliss  type  with  vacuum  dash- 
pots  which  give  a  very  sharp  cut-off.  The  high-pressure  and 
intermediate  cylinders  have  only  one  eccentric  and  wrist-plate, 
and  consequently  cannot  have  a  longer  cut-off  than  half  stroke 


390 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


under  the  control  of  the  drop  cut-off  mechanism.     The  low  - 
pressure  cylinder  has  two  eccentrics  and  two  wrist-plates,  and 


340 


300 


240 


200 


\ 


mpound, 


thout  jackets 


Trip 
without  j  a 


e, 


kets 


plejackets 
heads 


Triple,  jackets 
on  cylinder 
f  and  receiver 


Iplejakk, 

.Lvi  i«  A  ««, 


ets 
s  only 


10  20  30  40 

FIG.   81. 

the  admission-valves  can  be  set  to  give  a  cut-off  beyond  half 
stroke.     The  governor  is  arranged  to  control  the  valves  for 


ECONOMY  OF  STEAM-ENGINES.  391 

any  or  all  of  the  cylinders.  Each  cylinder  has  also  a  hand- 
gear  for  controlling  its  valves.  For  experimental  purposes 
the  governor  is  set  to  control  only  the  high-pressure  valve- 
gear,  when  the  engine  is  running  compound  or  triple-expan- 
sion. The  hand-gear  is  used  for  adjusting  the  cut-off  for  the 
other  cylinder  or  cylinders;  usually  the  cut-off  for  such 
cylinder  or  cylinders  is  set  to  give  a  very  small  drop  between 
the  cylinders.  This  arrangement  throws  a  very  small  duty 
on  the  governor,  so  that  by  the  aid  of  a  large  and  heavy  fly- 
wheel the  engine  can  be  made  to  give  nearly  identical  indi- 
cator-diagrams for  an  entire  test  during  which  the  load  and 
the  steam-pressure  are  kept  constant. 

The  main  dimensions  of  the  engine  are  as  follows: 

Diameter  of  the  high-pressure  cylinder 9     inches, 

intermediate         "         * 16 

"  "       low-pressure  24          " 

"  "       piston-rods 2T\      " 

Stroke 30 

Clearance  in  per  cent  of  the  piston  displacements: 

High-pressure  cylinder,  head  end,     8.83  ;  crank  end,    9.76 
Intermediate          "  "         "      10.4          "         "     10.9 

Low-pressure  "         "     11.25  "       8.84 

Results  of  tests  on  the  engine  with  the  cylinders  arranged 
in  order  to  form  a  triple-expansion  engine  are  given  in 
Table  XXXIII;  those  on  the  engine  with  the  small  and 
intermediate  cylinders  forming  a  compound  engine  are  given 
in  Table  XXXIV;  and  other  tests  with  the  tubular  reheaters 
in  use  are  given  in  Table  XXXV.  The  results  of  tests  in 
Tables  XXXIII  and  XXXIV  are  represented  by  the  diagram 
Fig.  8 1,  with  the  cut-off  of  the  high-pressure  cylinder  for 
abscissae  and  with  the  consumptions  of  thermal  units  per 
horse-power  per  minute  as  ordinates. 

The  most  important  investigation  which  has  been  made 


392  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

TABLE  XXXIII. 

TRIPLE-EXPANSION    EXPERIMENTAL  ENGINE  AT  THE  MASSA- 
CHUSETTS   INSTITUTE   OF    TECHNOLOGY. 

Trans.  Ant.  Soc.  Mech.  Engs.,  1892-1894;    Technology  Quarterly,  1896. 


Condition. 

Revolutions  per  minute. 

Per  cent  of  cut-off,  h'gh- 
pressure  cylinder. 

Boiler-pressure  by  gauge. 

Vacuum  in  condenser, 
inches  of  mercury. 

Barometer,  inches  of 
mercury. 

Steam  used  in  jackets, 
per  cent. 

u 

1 
i 

i 

140.8 
138.0 
125.4 
123.9 
114.7 
105.3 
103.5 

u 

01 

•: 

0 

a 
jj 

o 

<U  3 

H 

ss. 
c/5 

13.8 

'3-9 
13-7 
!3-7 
'4-3 
J4-5 
14.7 

8. 
ai  . 

•"TO 
ffi  3 

& 

.  V 

£5 

H| 

cd 

240 
241 

237 
239 
247 
250 

255 

h 

V  3 
*•* 

c^* 
K^ 

*! 

PS 
H'l 

cd 

i 

<u  <u 

M 
}l 

U 
V 

> 
'3 

i 

i 

£ 

Intermediate-pres- 
sure cylinder. 

g 

£ 

o 

B 

•a 
a 

0 

1 

c 

">, 
o 

V 

I 

5   4J 

o-o 
_J 

2 

4 

3 

I 

9 

e    • 
o  2 
2-S 
5.1 

£& 

8?.  93 
90.60 
9J'93 
91.55 
92.37 
84.87 

36  i 
35-0 
27-3 
27.0 
25.0 
21.9 

146.2 
14.7.0 

146.9 
146.7 
146.6 
145.2 

24.1 

24.7 
24-5 
25-4 
24-5 
24-3 

29.8 
3°-3 
29-9 
30.1 

3°-7 
30.1 

3-2 

2.5 
2.5 

3-2 

3-4 
3-5 

;;;; 

8.6 
8.8 
8-5 
9.8 
10.4 
"•3 



6.3 
5-4 
7.2 
8.1 

10.  I 

8.7 

233 
237 
231 
236 
240 
241 
255 
273 
274 

255 
237 
235 

86.70 
87-55 

14  .0 

2     .0 

8-3 

146.7 

26.0 

30.1 

6-5 

i5-3 



13.0 

67.4 

16.0 

274 

253 
235 
232 

10 

It 

32 

Ditto. 

84.23 
82.50 
82.13 

13-5 
20.5 
23.6 

145.2 
144.5 
145-3 

26.1 
26.2 
26.4 

30.0 
29.9 
30-1 

5-3 
4-S 
3-i 

2.6 

2.9 
3-o 
1.4 

3-2 

3.4 

2.9 

2.  I 
2.2 
1.4 

J-3 
i-4 

I  .2 
I  .  I 

"•3 
9.1 
8-5 

12.  I 

9.9 

9.8 

77.8 
101.9 
104.2 

14.7 
13-5 
13-3 

*3 

14 
15 
26 
«7 

18 

'9 

20 
21 

22 
23 

'-'4 

2 

27 
28 
^9 
30 
|1 
32 
33 
34 

P 

37 
3« 
39 
40 
4i 

Jackets  on 
cyTdrs  and 
receivers. 

91.20 
91.40 
91.82 
91.83 
92.17 
92.57 

36.1 
32.8 
29.3 
27-5 
25-9 
21.9 

M3-7 
143.6 
143-2 
147.1 
145-5 
143-7 

24.7 
25.0 
25-2 
24.7 
25-5 
26.4 

30.2 
30.2 
30-5 
30-3 
3°-4 
30.6 

x 

5.6 

4-7 
4-5 
6.8 

6.4 
7.1 
7.6 
8.9 

8.2 

7-i 

5-4 
4-3 
4-9 
3-i 
47 
4-1 

5-9 
6-4 
6.1 
7-3 
5-7 
7-7 

154.2 
145.1 
137.0 
128.8 
125.8 

I2O.2 

14.4 
14.1 
M-3 
14.1 
14.1 
14.6 

249 
244 
246 
242 
243 
256 

290 
273 

27.3 
269 
267 
265 
265 
267 

2^4 

240 

243 
237 
241 

2j'-' 

285 
277 
269 
269 
26l 
263 
262 
264 

c 
o 

!l 

2* 

3 

M 
u 

rt 
O 

55 

84-95 
84.03 
83.35 
82.40 
81.40 
81.05 
80.28 
80.32 

9.1 
13.9 
15.6 
20.7 
27-3 
29.7 
34-9 
35-6 

145-8 
144.5 
144.9 

H5-3 
144.2 

143-4 

M3-  * 
144.0 

256 
26.4 
25.6 
26.7 
24.7 
25-4 
250 
25.0 

30.0 
29.9 
29.8 

30.3 
29.7 
29.9 
30.2 
29.9 

7-7 
7-2 
6.8 
6.6 
7-7 
5-3 
5.0 
4.6 

.::.:: 

8.7 
8.6 

8.0 
8.0 
5-6 
6.8 
6.4 
7-4 

55-9 
69.4 
72.8 
84.2 
97-4 
101  .5 
109.4 
114.1 

16.6 

15-5 
JS-S 
15-1 
15.2 
15.° 
15-0 
15.2 

85.60 
85.62 
85.60 
84.22 
83-03 
82.92 
82.55 
83-32 
82.67 
81.78 
82.92 
81.52 
81.57 
81.40 
81.50 

8.4 
8-3 
10.6 
15-8 
21.3 

21.2 
21  .O 
24.1 
29-5 

28.7 
30-7 

31.8 
35-6 
33.8 

152.8 

153-3 
152.1 
152.8 
I52.O 
152.4 

153-° 
152.0 

I5L9 
152.0 
152.5 

I5L5 
152.0 
152.0 
i5T-9 

26.1 
26.1 
26.1 
2|.9 
26.3 
26.09 
26.02 
25.70 
25.6 
25.7 
26.0 
26.1 
26.O 
26.04 
25-9 

29-7 

53-? 
55-7 
60.6 
74-9 
85.8 
86.9 
87.8 
91.1 
99-9 
100.5 

102  .  4 

106.0 
108.2 

III  .2 
112.  2 

!7-3 
16.9 
16.2 
J5-4 
15-1 
J5  4 
15.2 
15-5 
iS-S 
15-2 
15.0 

^5-2 

14.9 
14,3 
15-1 

318 
3o6 
296 
287 
276 
281 
284 
280 
283 
275 
272 
278 
271 
274 
274 

3'8 
308 
297 
286 
277 
281 
284 
278 
280 
273 
272 
278 
271 
2/4 
274 

29-9 
29.8 

30-15 
30.0 

:..'".: 

3"-o 

29.9 
29.9 

30.1 
30.26 

ECONOMY  OF  STEAM-ENGINES. 


393 


TABLE  XXXIV. 

EXPERIMENTAL     ENGINE     AT     THE     MASSACHUSETTS    INSTI- 

TUTE   OF    TECHNOLOGY. 

COMPOUND;  CYLINDER  DIAMETERS  9  AND  24    INCHES;  STROKE  30  INCHES. 
Technology  Quarterly,  vol.  xi,  p.  43. 


Revolutions  per 
minute. 

Boiler-pressure 
by  gauge. 

Vacuum  in  con- 
denser, inches 
of  mercury. 

Barometer, 
inches  of  mer 
cury. 

Per  cent  of  cut- 
off, high-pres- 
sure cylinder. 

Steam  used  in 
jackets,  per 
cent. 

Horse-power. 

Steam  per  horse- 
power per 
hour. 

B.  T.  U.  per 

horse-power 
per  minute. 

I 
2 

82.72 

119-3 

24.7 

29.56 
29  80 

14.4 

5^-87 

fA   8<J 

iy-95 

359 

82.75 

119.0 

11:  \ 

19.27 

81  88 

2*  O 

63   89 

18.49 

81  62 

6 

6c  -16 

18.30 

i 

82.40 

26'! 

££ 
66.24 

18.07 

81  7^ 

26.1 

18.  17 

8 

81.30 
81  28 

119.2 

25-1 
26.4 

29.61 

*J 



71-27 
81.41 

18.14 
17.46 

327 

IO 

II 

81.00 
81.38 
80  80 

125.5 
124.8 

26.3 

26.5 

29.74 
29.63 
29  62 

28.1 
30.0 

81.78 
82.92 
87.07 

17.62 
'7-40 
18.01 

321 
323 

13 
14 

;i 

17 

82.83 
82.90 
83.20 
81.48 
81.12 

120.  6 
120.7 
118.9 
119.2 

119.5 

26.3 
26.3 

26.9 
26.0 

26.3 

30-  *7 
30.00 
29.40 
29.50 
29-39 

15.2 
14-5 
15.0 
25.6 
29.9 

17.4 
i5-4 
16.1 
12.4 
14.5 

69.2 
72.08 
72.61 

93-68 
98.32 

17.24 
16.  u 
16.21 
16.24 
16.73 

303 
284 
289 
289 
298 

18 
X9 

20 
21 

82-73 
82.90 
81.72 
8i.37 

100.2 
IOI  .O 
100-9 
IOI  .4 

26.6 
26.6 

26.3 

26.3 

29.49 
29.49 
29.49 
29.49 

16.3 
15.6 

24.0 
25.4 

19.2 

20.1 

»7-3 
19.6 

63.07 
63.19 
78-13 
80.47 

15.96 
'5-59 
16.16 
16.14 

282 

275 
284 
284 

TABLE  XXXV. 

TRIPLE-EXPANSION  EXPERIMENTAL  ENGINE  AT  THE  MASSA- 
CHUSETTS INSTITUTE  OF  TECHNOLOGY"  WITH  TUBULAR 
REHEATERS. 


Condition. 

olutions  per 
nute. 

cent  of  cut-off, 
Lfh-pressure 
Tinder. 

er-pressure 
gauge. 

uum  in  con- 
nser,  inches 
mercury. 

imeter,  inches 
mercury. 

Per  cent  of 
steam  used 
in  reheaters. 

se-power. 

m  per  horse- 
wer  per  hour. 

ai 
=  «f 

.  i-  ~ 

.  U.  per  H.  P. 
r  inin.  reduced 
26"  vacuum. 

•o 

c 

ts 

u-5  o 

c-o     rt-u"o 

S'o 

£ 

c 

«;  a. 

'f  a.ca 

a° 

X 

ou 

03          > 

H 

x 

X 

C/3 

aa 

05 

I 

3 
4 

Without 
steam  in 
reheaters. 

81.8 
81.8 
81.6 
81.2 

27 
27 

2Q. 

36 

146.7    26.4 
147.5   26-  1 
147.0  25.9 
148.2.  25.9 

30.6 
30-4 
30-5 
30.2 

88.6 
87-5 
89-7 
103.3 

16.0 
16.0 
16.0 
15-5 

200 
29I 
290 
282 

288 
281 



5 

Steam  in 

8s-  S 

10 

147.  2j     25.5 

30.0 



13 

66.  5 

15-7  ''      277 

273 

6 

first 

ig 

146.9  23.8 

30.2 



14 

84-9 

15-9        277 

262 

7 

reheater. 

81.4 

31 

146.11  25.8 

30.2 

12 

112.4 

15.0        266 

264 

8 

Ss.o 

8 

147.3  26.6 

3°-3 

IO 

7 

61.5 

15.5         269 

274 

9 

Steam  in 

84-S 

10 

146.9    26.2 

30-3 

12 

8 

74-8 

14.9  i      261 

260 

IO 

both 

82.4 

21 

147.1   25.3 

3°-4 

IO 

6 

95-7 

14.7         258 

252 

ii 

reheaters. 

81.9 

27 

147-7,  25.4 

30.1 

6 

9 

105.  q 

14-7  ;     259 

254 

12 

82.0 

28 

146.6;  25.7 

! 

30.2 

7 

8 

107.0 

14.5         256 

254 

394  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

on  this  engine  is  of  the  advantage  to  be  obtained  from  the 
use  of  steam  in  the  jackets.  Four  series  of  tests  were  made 
for  this  purpose:  (i)  with  steam  in  all  the  jackets  of  the 
cylinders  and  receivers,  (2)  with  steam  in  the  jackets  of  the 
cylinders,  both  heads  and  barrels,  (3)  with  steam  in  the 
jackets  on  the  heads  of  the  cylinders  only,  and  (4)  without 
steam  in  any  of  the  jackets. 

The  most  economical  method  of  running  the  engine  was 
with  steam  in  all  the  jackets  on  the  cylinders,  but  without 
steam  in  the  receiver-jackets,  as  shown  by  the  lowest  curve 
on  Fig.  81.  There  is  a  small  but  distinct  disadvantage  from 
using  steam  in  the  receiver-jackets  also.  This  fact  could  not 
be  surely  determined  from  any  pair  of  tests,  for  the  difference 
is  not  more  than  two  per  cent,  and  is  therefore  not  more  than 
the  probable  error  for  such  a  pair  of  tests,  but  a  comparison 
of  the  two  curves  on  Fig.  81  representing  tests  under  the  two 
conditions  gives  conclusive  evidence  with  regard  to  this 
point.  It  may  not  be  improper  in  this  connection  to  call 
attention  to  the  three  points  below  the  lowest  curve  and 
not  connected  with  it;  they  represent  tests  which  were  made 
after  the  nine  tests  represented  by  points  joined  to  the  curve, 
and  when  some  additional  non-conducting  covering  had  been 
applied  to  the  piping  and  valves  of  the  engine.  Here  the 
slight  gain  from  reduced  radiation  is  made  manifest,  though  it 
is  too  small  to  be  taken  into  account  in  making  comparisons 
of  the  different  conditions  of  running  the  engine. 

From  the  diagram  Fig.  81  the  best  results  with  steam  in 
all  the  jackets  of  the  cylinders  and  without  steam  in  any  of 
the  jackets  are  233  and  274  B.  T.  U.  per  horse-power  per 
minute,  and  the  gain  from  the  use  of  the  steam  in  the  jacket 
is 

274  —  233 

-  X  loo  =  15  per  cent. 
274 

These  heat-consumptions  correspond  to  13.8  and  15.2  pounds 
of  steam  per  horse-power  per  hour,  so  that  on  the  basis  of 


ECONOMY  OF  STEAM-ENGINES.  395 

steam-consumption  the  gain  from  the  use  of  steam  in  the 
jackets  would  appear  to  be  only  9  per  cent,  instead  of  the 
actual  gain  of  15  per  cent.  This  large  difference  is  due  to  the 
large  percentage  of  steam  used  in  the  jackets,  amounting  in 
all  to  17  or  1 8  per  cent  of  the  total  steam-consumption.  The 
steam  used  in  an  individual  jacket  is,  however,  not  excessive, 
being  about  2.5  per  cent  in  the  jackets  of  the  high-pressure 
cylinder  and  7  or  8  per  cent  in  the  jackets  of  each  of  the  other 
two  cylinders. 

The  effect  of  jacketing  the  heads  of  the  cylinders  only  is 
surprisingly  small,  as  from  the  diagram  the  best  result  is  262 
B.  T.  U.  per  horse-power  per  minute,  which  compared  with 
the  best  result  without  steam  in  any  of  the  jackets  gives  a 
gain  of  only 

274  —  262 


274 


X  100  =  4  per  cent. 


The  correspondence  between  this  result  and  the  experiments 
by  Callendar  and  Nicolson  on  the  action  of  the  cylinder-walls, 
has  already  been  pointed  out. 

The  tests  recorded  in  Table  XXXIV  were  made  on  this 
same  experimental  engine  using  only  the  smallest  and  the 
largest  cylinders  to  form  a  compound  engine.  Tests  I  to  12 
were  made  without  steam  in  any  of  the  jackets;  tests  13  to 
17  were  made  with  steam  in  the  jackets  of  the  low-pressure 
cylinder  only;  while  tests  18  to  21  were  made  with  steam  in 
the  jackets  of  both  cylinders  and  in  the  receiver  jacket. 
The  first  series  of  twelve  tests  without  steam  in  the  jackets  is 
represented  by  the  highest  curve  on  Fig.  81.  The  results  of 
tests  with  steam  in  the  jackets  are  not  represented  on  the 
diagram  to  avoid  confusion;  they  are  not  numerous  nor  im- 
portant enough  to  warrant  drawing  another  diagram.  The 
curve  representing  tests  without  steam  in  the  jackets  does 
not  show  a  minimum,  and  indicates  that  too  large  a  total 
expansion  for  this  method  of  running  the  engine  was  used. 
The  tests  with  steam  in  all  the  jackets  show  a  somewhat  poorer 


39  THERMODYNAMICS   Of    THE   STEAM-ENGINE. 

economy  than  the  engine  has  when  running  triple-expanding 
without  steam  in  the  jackets.  We  cannot  draw  any  definite 
conclusions  concerning  the  use  of  jackets  from  these  tests. 
The  evidence  they  present  with  regard  to  the  proper  ratio  of 
high-  and  low-pressure  cylinders  will  be  considered  later. 

Experimental  Engine  at  Cornell. — The  triple-expansion 
experimental  engine  in  the  laboratory  of  Sibley  College, 
Cornell  University,  was  built  by  the  makers  of  the  engine  in 
the  laboratory  of  the  Massachusetts  Institute  of  Technology 
and  resembles  it  in  all  respects  except  that  its  stroke  is  six 
inches  longer.  The  tests  on  the  engine  recorded  in  Table 
XXXVI  are  therefore  especially  valuable,  as  they  may  be 
compared  directly  with  those  made  on  the  engine  at  the 
Institute. 

Tests  33  to  37  were  made  with  the  engine  running  triple- 
expanding  without  steam  in  any  of  the  jackets;  tests  38  to  44 
were  made  with  steam  in  all  the  jackets  of  cylinders  and 
receivers  except  the  jackets  on  the  low-pressure  cylinder. 
Though  differently  arranged,  the  general  effect  of  the  jackets 
appears  to  be  similar  to  that  of  the  jackets  on  all  three 
cylinders  of  the  Institute  engine.  The  steam-pressure  on  the 
Cornell  engine  was  only  115  pounds  per  square  inch,  while 
that  of  the  Institute  engine  was  150  pounds.  Nevertheless 
the  steam-  and  heat-consumption  for  the  two  engines  both 
with  and  without  steam  in  the  jackets  is  nearly  identical,  and 
the  condensation  of  steam  in  the  jackets  under  the  first  con- 
dition is  nearly  the  same  percentage  of  the  total  steam-con- 
sumption. Such  a  result  is  most  satisfactory,  as  it  proves 
conclusively  that  the  tests  on  both  engines  are  entirely  reliable 
and  free  from  personal  error. 

The  Cornell  engine  was  also  tested  using  the  small  cylin- 
der only  as  a  simple  engine,  and  again  using  the  small  and 
intermediate  cylinders  to  form  a  compound  engine.  With 
both  arrangements  tests  were  made  using  steam  in  the  jackets 
and  without  steam  in  the  jackets. 

As  a  simple  engine,  the  proportions  of  the  cylinder  appear 


ECONOMY   OF  STEAM-ENGINES. 


397 


TABLE  XXXVI. 

EXPERIMENTAL    ENGINE    AT    CORNELL   UNIVERSITY. 

CYLINDER    DIAMETERS,    Q,    l6,    AND    24    INCHES;    STROKE    36    INCHES. 

Trans.  Am.  Soc.  Mech.  Engs.,  vol.  xvi,  p.  913. 


cj 

. 

per  minui 

xpansion 

•Sl-s 

V        C 

%  «  — 

"o 

1 
u 

c 

1 

a 

u 

& 

c 

•se-powei 

rse-powe 
ounds. 

V 

1! 

Condition. 

en 

w 

3  u   V 

•'    •     ~ 

4~ 

u 

en 

0 

.c 

evolution 

umber  of 

eam-pres 
atmosph< 
per  squa 

arometer 
mercury, 

acuum,  ii 
mercury. 

oisture  in 
per  cent. 

:eam  usec 
per  cent. 

idicated  h 

If 

|g. 

T.  U.  pe 
power  pe 

tf 

2 

M 

05 

> 

S 

(/i 

c 

05 

x 

83.8 

30 

95-8 

29.2 

23-5 

0.7 

73-1 

25.8 

2 

9  X  36 

84-5 

3-o 

96.3 

29.2 

23-9 

o-7 

62.5 

24.9 

3 

4 

Simple  without 

86.3 
87.0 

I'.l 

97.1 
97.1 

29.2 
29.2 

23-9 
24.4 

0.7 
0.8 

.::::.' 

52-4 
39-9 

23.5 
24.9 

421 

5 

steam  in 

85.0 

8.6 

93-7 

29.2 

24.7 

0.7 

3°-3 

25.8 

6 

jackets. 

87-5 

12.  0 

100.8 

29.2 

24.7 

0.9 



19.1 

32-9 

7 

82.0 

I4.2 

97-4 

29.2 

24.7 

0.8 

9-5 

47-5 

8 

83.6 

2-3 

95-7 

29-3 

24.2 

0-7 

3.7 

71.9 

25.6 

9 

84-5 

3-1 

96.7 

29-3 

24.7 

°7 

3-9 

62.4 

25-5 

10 

Simple  with 

85-4 

4-4 

97-7 

29-3 

24.8 

0.8 

50.2 

23.1 

411 

ii 

steam  in 

86.3 

6.3 

98.9 

29.3 

24.9 

0.8 

6.7 

40.2 

23-9 

12 

jackets. 

87.0 

9.0 

96.9 

29-3 

24.8 

0.7 

9-7 

30.3 

24.0 

13 

'4 

87.7 
88.2 

12.5 
14.2 

102.4 
99-3 

29.3 
29-3 

24.8 
24.7 

0.8 
0.8 

13-4 
24.6 

19.9 
9.0 

3:1 

:s 

18 

Compound 
without  steam 
in  jackets. 

83-7 
84.6 
85-6 
81.7 
87.4 

7.8 

IO.2 

16.2 

26.5 

39-6 

106.4 
106.0 
105.3 
107.6 
108.5 

29.3 
29.3 
29-3 
29-3 
29-3 

21.7 
21.5 

22.0 
21-5 
22.5 

0.8 
0.8 
0.7 

0.2 
0.0 

:::::: 

97-3 
78.7 
57-7 
35-7 
24.6 

l! 

16.5 
19.2 

22.8 

292 

20 

88.2 

46.4 

113.7 

29.3 

22.0 

o.o 

11.4 

35-6 

21 

16  X  36 

84.4 

7.6 

106.9 

29.4 

22.6 

o  3 

ii.  i 

99.8 

18.5 

22 

85.5 

11.4 

106.3 

29.4 

22.7 

0-3 

14.3 

77-4 

18.2 

316 

23 
24 
25 

Compound  with 
steam  in  h.p. 
and  receiver 

86.0 
87-2 
87-7 

17.2 
32  o 
41.4 

112.7 

112.  I 

"43 

29-3 
29.3 
29  3 

21*5 
21  .8 

23.8 

0.8 

0.8 

14.3 
3:? 

58.2 
35-6 
25.2 

18.5 

20.2 
21.7 

26 
27 

jackets. 

87.8 
88.0 

43-1 

46.4 

112.4 
"3-4 

29-3 
29-3 

23.5 
23-3 

0.8 
0.9 

29.2 
30.5 

20.0 

16.2 

22.5 
26.2 

23 

85.0 

9.0 

94-5 

*I4.4 

*II.3 

0.7 

18.9 

76.9 

18.0 

29 

Compound, 

85  3 

10.  I 

95-2 

14.5 

ii.  6 

0.7 

14.6 

J7-3 

30 

steam  in  all 

85.1 

10.3 

94-5 

0.8 

15-5 

76^2 

31 

jackets. 

85.4 

12-5 

95-4 

14.4 

ii.  6 

0-5 

13.8 

72.4 

i6.'3 

284 

32 

85-7 

13.6 

103.0 

14.2 

II.  2 

0.9 

18.0 

18.2 

33 

84.7 

27  .  3 

114.  i 

29.  3 

23.4 

88.6 

34 

35 
36 

Triple  without 
jackets. 

u^..  / 

85-9 
86.9 
86.8 

36.6 

"5-4 
114.7 
"5-0 

29.3 
29.3 

29-3 

22.7 
22.7 
22.6 

66.1 
46.1 

35-5 

18.0 
19  9 
24.1 

275 

37 

88.2 

92.1 

114.1 

29-3 

22.7 



22.7 

27-5 

38 
39 

Triple  with 

83-8 
85.0 

15.8 

21.9 

116.3 
116.1 

29-3 
29-3 

24.2 
24.3 

16.7 

21.8 

141.4 
112.7 

;s-3 

237 

steam  in  h.p. 

85-5 

29.4 

114.1 

29-3 

23-3 

24.4 

89.8 

14.9 

41 

and  int.  and 

86.2 

48.5 

"5-4 

29-3 

24.1 



27.9 

63.0 

16.8 

42 

receiver 

87.0 

69.0 

114.7 

29-3 

22.9 



31.2 

45-6 

17  7 

43 

jackets. 

870 

88.1 

115.0 

29-3 

22.1 

33-8 

3^-9 

21.  1 

44 

88.0 

96.7 

114.1 

29.2 

21.6 

36-8 

26.2 

24.1 

*  Pounds  per  square  inch. 


398  THERMODYNAMICS  OF   TEE   STEAM-ENGINE. 

to  be  unfortunate,  for  the  economy,  measured  either  in  terms 
of  steam  per  horse-power  per  hour,  or  in  terms  of  B.  T.  u. 
per  horse-power  per  minute,  is  poor,  even  allowing  for  the 
low  vacuum  in  the  condenser.  The  condensation  in  the 
jackets  appears  to  be  normal,  showing  that  the  jackets  were 
active,  and  were  not  using  an  excessive  amount  of  steam,  and 
yet  the  gain  from  using  steam  in  the  jackets  is  trivial, 
amounting  to  only 

42 1  —  4 1 1 
— — x  ioo  =  3  per  cent. 

The  detailed  report  by  Professor  Carpenter  shows  that 
the  simple  engine  has  nearly  as  much  condensation  and 
re-evaporation  with  steam  in  the  jackets  as  without,  except 
for  tests  with  a  very  early  cut-off.  As  the  jackets  did  not 
have  much  effect  on  the  action  of  the  cylinder-walls  they 
could  not  be  expected  to  reduce  the  steam-consumption. 
For  tests  with  an  early  cut-off,  however,  the  jackets  did 
reduce  condensation  and  improved  the  economy.  Thus 
tests  6  and  13  appear  to  show  a  large  gain  from  the  use 
of  the  jackets;  but  a  similar  gain  can  be  obtained  by 
lengthening  the  cut-off.  This  gives  another  illustration  of 
the  futility  of  trying  to  find  the  advantage  of  using  steam- 
jackets  from  a  pair  of  tests  with  and  without  steam  in  the 
jackets. 

Three  series  of  tests  were  made  on  the  engine  running 
compound,  using  the  small  and  intermediate  cylinders. 
Tests  15  to  20  were  made  without  steam  in  any  of  the 
jackets  and  tests  28  to  32  were  made  with  steam  in  all  the 
jackets.  Again,  tests  21  to  27  were  made  with  steam  in  the 
jackets  of  the  high-pressure  cylinder  and  the  intermediate 
receiver,  but  with  much  worse  results  than  when  no  steam 
was  used  in  any  of  the  jackets.  It  is  a  question  whether  the 
jacketing  was  not  overdone  in  both  series  of  tests  with  steam 
in  the  jackets,  for  the  percentage  of  condensation  of  steam  in 
the  jackets  is  large,  if  not  excessive.  If  the  steam-consump- 


ECONOMY  OF  STEAM-ENGINES.  399 

tion  is  taken  as  the  basis  of  comparison  there  appears  to  be 
little  gain  from  the  use  of  steam  in  the  jackets;  for  example, 
the  steam-consumption  for  test  17  is  16.5  pounds  per  horse- 
power per  hour,  and  it  is  16.3  for  test  31.  But  a  comparison 
of  the  thermal  units  per  horse-power  per  minute  for  these  same 
tests  shows  a  gain  of 

202  —  275 

- X  ioo  =  6  per  cent. 

It  is  probable  that  a  better  result  could  be  obtained  by 
jacketing  the  cylinders  and  not  the  intermediate  receiver,  or 
perhaps  by  jacketing  the  low-pressure  cylinder  only. 

Tests  on  Pumping  -  engine  at  Laketown.  —  Table 
XXXVII  gives  the  results  of  tests  made  on  a  triple-expansion 
pumping-engine  at  Laketown,  Indiana,  to  show  the  effect 
of  using  steam  in  jackets  on  the  cylinders  and  in  reheaters 
placed  in  the  intermediate  receiver.  Taking  the  steam-con- 
sumption as  the  basis  of  comparison,  there  appears  to  be  only 
a  trivial  gain  from  the  use  of  steam  in  the  jackets.  But  when 
the  comparison  is  made  using  thermal  units  per  horse-power 
per  minute  the  gain  is 

264  —  253 

— g — '•  -  X  ioo  =  4  per  cent. 

It  appears  that  as  good  a  result  is  obtained  when  steam  is 
used  in  the  jackets  of  the  intermediate  and  low-pressure 
cylinders  as  when  steam  is  used  in  all  the  jackets  and  the 
reheaters. 

But  the  economy  of  this  engine  is  poor — no  better  than 
that  of  the  experimental  engine  at  the  Massachusetts  Institute 
of  Technology,  which  develops  only  half  the  power  and  is 
only  a  fifth  as  large.  It  is  difficult  to  account  for  this  poor 
performance,  for,  though  the  stroke  is  short,  the  valves,  which 
are  of  the  Corliss  type,  are  in  the  cylinder-heads,  so  that  the 
clearance  is  not  excessive. 


400  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

TABLE  XXXVII. 

TRIPLE-EXPANSION    HORIZONTAL    PUMPING-ENGINE 
AT    LAKETOWN,    INDIANA. 

CYLINDER    DIAMETERS    24^,    34,    AND    54    INCHES;    STROKE    36    INCHES. 

By  Professor  J.  E.  DENTON,  Trans.  Am.  Soc.  Mech.  Engs.,  vol.  xiii,  p.  1340. 


i 

2 

3 

4 

5 

6 

7 

8 

i« 

c 

0 

Steam  in  all  jackets  and 

.-;  ca 

._; 

in  reheaters. 

.2  2  £ 

G  £ 

Jj£j 

ill 

it 

'"! 

& 

c/5 

* 

Duration       .         

8 

5 

5 

6 

6 

8 

12 

o 

Revolutions  per  minute     . 

27.8 
36 

27.6 

21 

28.3 

22 

27-3 
23 

27.7 
23 

28.0 

22 

27.9 
23 

27.7 

31 

Cut-off  ,  h.  p  cylinder  percent.... 

mt         do             do 

39 

41 

43 

4° 

4° 

43 

43 

40 

1.  p.       do.             do  

44 

47 

53 

47 

47 

39 

52 

45 

Pressures,  pounds  per  square  inch  above 

atmosphere: 

Boiler   

II.3 

151 

*5* 

*5* 

150 

152 

I  cj 

I  ci 

High-pressure  jacket                 .   .. 

"3 

151 

151 

151 

150 

Intermediate-      and      low  -  pressure 

jackets  and  receivers    

"3 

135 

72 

67 

43 

62 

75 

Vacuum,  inches  of  mercury  

26.2 

26.1 

26.7 

26.  i 

26.2 

26.2 

26.2 

26^1 

Barometer,  inches  of  mercury      
Temperature  jacket-water,  degrees  F.  .  .  . 
Per  cent  of  moisture  in  steam  

29.8 
336 

2.2 

28.8 
356 

2 

29.4 
308 

2 

28.7 
300 

2.5 

29-3 
280 

2-5 

29.1 
299 
2.4 

29-3 

310 

2 

29.1 

2 

Percentage  of    condensation   in    jackets 

and  reheaters  

18 

28 

23 

1.9 

ig 

23 

21 

Efficiency  of  mechanism  

0.94 

0.92 

°-95 

0.94 

o  94 

°-95 

0.93 

O    QI 

Horse-power,  indicated   
Steam  per  horse-power  per  hour,  pounds 
B.  T.  U.  per  horse-  power  per  minute     . 

322 

323 
13-8 

248 

327 
14.0 

253 

3»7 

250 

322 
13  8 
253 

313 
14.1 
256 

323 
13.8 

252 

328* 
I4.I 
264 

Gain  from  Using  Steam-jackets. — Reviewing  all  the 
tests  on  engines  with  and  without  steam  in  the  jackets,  bear- 
ing in  mind  the  discrepancies  which  have  been  pointed  out 
and  not  satisfactorily  explained,  it  appears  to  be  conservative 
to  say  that  from  5  to  10  per  cent  may  be  saved  by  jacket- 
ing simple  condensing-engines  and  compound  condensing- 
engines,  and  that  from  10  to  15  per  cent  may  be  saved  by 
jacketing  triple-expansion  engines,  provided  that  these  con- 
clusions shall  not  apply  to  engines  of  more  than  300  horse- 
power. Most  of  the  tests  quoted  are  on  engines  which  do  not 
develop  more  than  150  horse-power. 

The  saving  on  massive  engine^  of   1000  horse-power  or 


ECONOMY   OF  STEAM-ENGINES.  4OI 

more  is  likely  to  be  smaller,  and  very  large  engines  may 
derive  no  benefit  whatever  from  steam-jackets. 

The  saving  from  the  use  of  jackets  on  small  engines  of 
five  or  ten  horse-power  may  amount  to  25  per  cent  or  more, 
Isherwood  found  a  gain  of  about  30  per  cent  from  using  steam 
in  the  jackets  on  an  engine  5  inches  in  diameter  by  10 
inches  stroke  and  developing  one  and  a  half  horse-power. 
Such  engines  are  seldom  if  ever  provided  with  jackets,  as  the 
total  fuel-consumption  is  of  little  importance,  and  simplicity 
and  low  first  cost  are  more  considered  than  economy  of 
steam-consumption. 

Intermediate  Reheaters. — Many  compound  and  triple- 
expansion  engines  have  some  method  of  reheating  the  steam 
on  its  way  from  one  cylinder  to  another.  Notable  examples 
are  the  Leavitt  pumping-engines,  for  which  results  are  given  in 
Table  X.  The  ract  that  these  engines  give  the  best  economies- 
recorded  for  engines  using  saturated  steam  lead  to  the  infer- 
ence that  such  reheaters  may  be  used  to  advantage.  The 
only  direct  evidence,  however,  is  not  so  favorable,  for,  as  has 
been  pointed  out  on  rage  394,  there  was  found  a  small  but 
distinct  disadvantage  from  using  steam  in  double  walls  or 
jackets  on  the  intermediate  receivers  of  the  experimental 
engine  at  the  Massachusetts  Institute  of  Technology.  It 
appears  that  this  engine  gives  the  best  economy  when  steam 
is  supplied  to  the  jackets  on  the  cylinders  and  not  to  the 
jackets  on  the  reheaters,  and,  further,  that  when  steam  is  used 
in  the  receiver-jackets  the  steam  in  the  low-pressure  cylinder 
shows  signs  of  superheating,  which  may  be  considered  to 
indicate  that  the  use  of  the  steam-jacket  is  carried  too  far. 

After  the  tests  referred  to  were  finished  the  engine  has 
been  furnished  with  reheaters  made  of  corrugated-copper 
tubing,  so  arranged  that  one-third,  two-thirds,  or  all  of  the 
reheating-surface  can  be  used,  when  desired.  Table  XXXVr 
page  393,  gives  the  results  of  tests  made  on  the  engine  with 
and  without  steam  in  the  reheaters;  in  these  tests  the  entire 
reheating-surface  was  used  when  steam  was  supplied  to  a 


402  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

reheater;  the  effect  of  using  part  of  the  reheating-surface 
remains  to  be  determined. 

For  some  reason  the  heat-consumption  when  no  steam  was 
used  in  the  reheaters  is  somewhat  greater  than  that  given  in 
Table  XXXIII  for  the  engine  without  steam  in  any  of  the 
jackets;  the  difference,  however,  is  not  more  than  two  or  two 
and  a  half  per  cent  and  cannot  be  considered  of  much  impor- 
tance. It  is  clear  from  the  table  that  there  is  advantage 
from  using  one  reheater  and  still  more  from  using  two.  If 
the  heat-consumption  for  the  engine  without  steam  in  the 
jackets  and  without  steam  in  the  reheaters  (taken  from  Table 
XXXIII)  is  assumed  to  be  274  B.  T.  u.  per  minute,  then  the 
gain  from  using  the  reheaters  appears  to  be 

274  —  252 

-  X   ioo  =  8  per  cent, 
2  74 

which  is  scarcely  more  than  half  the  gain  from  using  steam  in 
the  jackets.  These  tests  cannot  be  considered  conclusive,  as 
they  are  too  few  and  refer  only  to  one  engine. 

Willans's  Tests.— Tables  XXXVIII  to  XLII  give  the 
results  of  a  very  extensive  investigation  by  Mr.  Peter  Willans 
on  a  peculiar  engine,  which  he  designed  to  run  at  high  speed 
and  give  a  good  economy.  His  success  is  shown  by  the  fact 
that  one  of  his  engines  developing  only  30  horse-power  used 
12.7  pounds  of  steam  per  horse-power  per  hour,  as  given  in 
Table  X. 

Willans's  tests  covered  a  wide  range  of  conditions,  includ- 
ing variations  of  steam-pressures,  number  of  expansions, 
speed  of  rotation,  both  with  and  without  condensation,  for 
his  engine  when  run  single,  compound,  or  triple-expanding; 
it  is  consequently  convenient  to  describe  his  engine  and 
discuss  his  tests  before  considering  the  effects  of  the  various 
conditions  named  on  the  economy  of  steam-engines. 

The  engine  is  a  single-acting,  vertical,  three-cylinder, 
triple-expansion  engine,  with  three  pistons  on  a  continuous 
piston-rod.  The  piston-rod  is  made  hollow  and  serves  as  a 


ECONOMY   OF  STEAM-ENGINES. 


403 


TABLE  XXXVIII. 

TESTS    ON   WILLANS    ENGINE. 

SIMPLE  NON-CONDENSING. 


4 

i 

minute. 

Pressures,  pounds  per 
square  inch. 

c 

Steam  per 
horse-power 
per  hour, 
pounds. 

O 

C 
0) 

Per  cent 
of  water  in 
cylinder. 

3 
C 

i 

c 

8 

• 

3 

uration,  m 

evolutions 

I 

11 

3  sn 

arometer. 

oiler  above 
atmosphere 

ack-pressur 
absolute. 

orse-pow  er 

k 

-•    Is  8  8 
1    ['III 

• 

1 

a 

t  cut-off. 

5  £ 

W              (V 

(J 

K 

H 

m 

< 

at. 

< 

< 

x 

1  80 

393 

O.6o 

14-5 

36.3 

14.8 

i6.s 

42  8 

81 

12 

IO 

2 

270 

408 

0.44 

51.0 

14-5 

20.0 

36.0 

28.6 

80 

19 

18 

3 

242  i    409 

0-34 

14.6 

74.0 

15-4 

25-5 

32.6 

23.0 

71 

27 

19 

4 

169 

403 

0.30 

14.7 

85.0 

15-4 

26.8 

29.7 

21  .2 

72 

24 

19 

5 

180 

400 

0.26 

14.8 

97.0 

15.6 

.,1.6 

26.9 

19.2 

25 

*9 

6 

176 

39« 

0.24 

14.6 

IIO.O 

15-4 

31-5 

27.8 

I8.7 

67 

31 

23 

7 

298 

406 

O.22 

14.7 

122.  O 

15-6 

33-6 

26.0 

17.9 

69 

30 

22 

8 

270 

408 

0.44 

H-S 

51.0 

14-5 

19.8 

36.0 

28.6 

80 

ig 

18 

9 

J53 

201 

0.44 

14.6 

44-0 

15-2 

9-3 

41-8 

29    2 

70 

24 

18 

IO 

122 

III 

o  44 

14.4 

40.2 

14-7 

6-5 

46.0 

29.4 

64 

35 

29 

ii 

242 

409 

o-34 

14.6 

74.0 

15-4 

25-5 

32.6 

23.0 

71 

27 

I9 

12 

152             205 

o-34 

M-5 

66.5 

15.1 

14.1 

34-4 

22-5 

65 

34 

23 

13 

127  ;     113 

0-34 

14.4 

62.0 

14.7 

7-9 

40.7 

22-9 

56 

46 

33 

14 

1  80 

401 

0.26 

14.8 

97.0 

15-6 

3'-  6 

26.9 

19.2 

72 

25 

Ig 

15 

118 

223 

0.26 

14.7 

84.7 

15-5 

16.8 

27.8 

19.7 

71 

25 

20 

16 

178 

I23 

0.26 

15-0 

80.0 

IO.O 

19.6 

58 

43 

29 

17 

298 

406 

0.22 

14.7 

122.0 

15-0 

33-6 

26.0 

17.9 

69 

3° 

21 

18 

119 

224 

O.22 

15.0 

112.  O 

*5-5 

20.5 

30.2 

17-7 

58 

42 

26 

19 

123 

138 

O.22 

14.7 

I05-4 

'5-5 

i3-i 

31.2 

17.7 

57 

«          3- 

TABLE  XXXIX. 

TESTS   ON    WILLANS    ENGINE. 

SIMPLE    CONDENSING. 


1 

3 

t 

Pressures,  pounds  per 
square  inch. 

.e-power. 

Steam  per 
horse-power 
per  hour, 
pounds. 

iciency. 

Per  cent 
of  water  in 
cylinder. 

b 

• 

Duration, 

Revolutiol 
minute. 

Cut-off. 

Barometer 

At  steam- 
chest, 
absolute 

Back- 
pressure 
absolute 

Indicated 

Actual. 

Required  1 
perfect 
engine. 

Percentage 

At  cut-off. 

At  end  of 
stroke. 

i 

•39 

382 

o-S 

14.6 

64.7 

I.O 

31.6 

25.7 

II  .2 

44 

16 

20 

2 

no 

380 

°-5 

15-1 

55-i 

I.O 

27.2 

25.2 

ii  5 

46 

17 

15 

3 

173 

381 

o-5 

14«7 

44.8 

I.O 

21.9 

26.7 

II  .2 

42 

21 

19 

4 

162 

382 

o-5 

15-0 

0.9 

i6.r 

28.9 

12.  I 

42 

24 

20 

5 

181 

385 

0.5 

15-0 

25.0 

0.9 

"•5 

30.0 

12.8 

25 

18 

6 

191 

3?8 

o-5 

15.0 

20.0 

0.8 

9.1 

29.4 

!3-4 

46 

23 

23 

7 

128 

383 

0.29 

'5- 

85.1 

i  .0 

33-2 

22.2 

10.3 

47 

25 

19 

8 
9 

1  86 

382 

0.29 
0.29 

15.1 
15- 

75'1 
65.1 

I.O 

0.9 

29.0 
24.8 

23-4 
24.0 

10.5 
10.6 

45 
44 

28 
28 

23 

22 

IO 

130 

378 

O.2Q 

45-o 

0.8 

16.8 

26.2 

II.  0 

42 

33 

23 

ii 

146 

382 

O.29 

15- 

25-1 

0.8 

9.18 

28.2 

12.  O 

43 

39 

30 

12 

138 

380 

O.29 

»5- 

20.  i 

0.9 

6.9 

30.0 

13.2 

44 

39 

24 

404 


THERMODYNAMICS  OF   THE   STEAM-ENGINE 


TABLE  XL. 

TESTS    ON    WILLANS    ENGINE. 

COMPOUND  NON-CONDENSING. 


Steam  per 

. 

3 

Point  of 
cut-off. 

Pressures,  pounds 
per  square  inch. 

<D 

lorse-power 
per  hour, 

>» 

§ 

O 

Per  cent  of  water 
in  cylinder. 

§ 

a 

1 

pounds. 

t! 
i 

3 

! 

g 

3 

w  u* 

i 

1 

* 

V 

1) 

o. 

d  . 

d. 

- 

§ 

§  <D 

w  jj 

u 

JO'S. 

s  a 

•a 

"O  •"  a] 

H 

rt 

JS  w 

—'  <u 

,—  I    U 

0 

'-M 

3 

sj 

UT3 

Id 

rt  g 

k| 

<u 

•3      &&£ 

a 

X    C 

1 

0 

•§£ 

^ 

3 

o 

«  a 

Aj 

1 

3      :  Pr1  D  n 

?'•= 

9  = 

£J; 

3 

u 

•—   U 

O  « 

rt 

8 

3  0 

P 

* 

ffi 

J 

PQ 

PQ 

PQ 

- 

<    & 

PH 

U 

g 

M 

I 

1  80 

400 

0.6 

0.6 

15-0 

80.2 

15-8 

24.9 

26.2 

21.2 

81 

5 

15 

14 

2 

123 

402 

0.6 

0.6 

15.0 

9°-5 

iS-4 

29.1 

24.2 

19.9 

82 

5 

15 

3 

177 

398 

0.52 

0.6 

14-6 

90.4 

,5.6 

26.1 

24-5 

I9.6 

80 

8 

17 

15 

4 

118 

402 

0.52 

0.6 

14.6 

100.5 

30.0 

23.0 

18.6 

81 

6 

21 

5 

364 

405 

0.47 

0.6 

14.7 

104.6 

15.0 

28.7 

23.8 

18.7 

82 

10 

16 

T5 

6 

123 

403 

0.47 

0.6 

14.9 

113-9 

iS-7 

33-o 

21.4 

17.7 

83 

IO 

16 

7 

121 

403 

0.43 

0.6 

15-0 

113.0 

!5-7 

31.0 

21.4 

17.8 

83 

II 

13 

17 

8 

181 

403 

0-43 

0.6 

15-0 

124-5 

15.4 

34-7 

20.8 

16.8 

81 

II 

20 

18 

9 

124 

404 

°-39 

0.6 

14.9 

124.8 

15-8 

21.3 

16.9 

79 

13 

2O 

16 

IO 

189 

406 

0-39 

0.6 

14.8 

I35--4 

'5-4 

P-  3 

20.4 

16.3 

80 

12 

19 

.8 

ii 

306 

402 

0.36 

0.6 

14.7 

133-6 

15-2 

33-3 

20.3 

16.3 

80 

14 

17 

i  7 

12 

184 

399 

0.36 

0.6 

14.6 

143-7 

iS-4 

36.6 

20.  o 

79 

14 

20 

18 

13 

1  20 

4°5 

0-33 

0.6 

14.4 

15.2 

36.4 

19-7 

15^6 

79 

IS 

20 

18 

14 

179 

404 

0.6 

14.1 

i55-o 

15.0 

38.6 

19-5 

15.2 

78          15 

21 

20 

15 

3°7 

402 

0.31 

06 

37-0 

19.6 



....       19 

IO 

177 

401 

0.31 

0.6 

14.5 

165  .0 

14.9 

39-6 

IQ.2 

14.0 

77 

17 

21 

2O 

~IT~ 

1  86 

407 

0.47 

0.6 

15-0 

134-8 

iS-5 

40.0 

20.8 

,63 

79 

9     !      20 

«9 

18 

182 

405 

0-43 

0.6 

15-0 

i35-o 

15.0 

38.0 

20.5 

16.3 

80 

II 

2O 

'9 

'9 

itg 

406 

0-39 

0.6 

14.8 

135-4 

15-4 

36.3 

20.3 

16.3 

80 

12 

19 

18 

20 

306 

402 

o.  36 

0.6 

14.7 

133-7 

iS-i 

33-3 

20.3 

16.3 

80 

14 

17 

17 

21 

182 

403 

0-34 

0.6 

14-4 

i35.o 

iS-4 

32-8 

20.0 

16.2 

81 

14 

16 

*•( 

22 

180 

400 

0.31 

c.6 

14.2 

135-0 

14.8 

31.2 

2O.3 

16.3 

80 

18 

19 

ij 

23 

200 

404 

0.23 

0.6 

14.8 

135-5 

15-4 

23.0 

23.I 

16.4 

7i 

=5 

18 

T4 

24 

I23 

401 

0.60 

0.6 

14.9 

9°  -5 

15.4 

29.1 

24.2 

19.9 

82 

5 

15 

14 

25 

123 

210 

0.60 

0.6 

14.8 

85.2 

15.5 

16.7 

25-3 

77 

13 

25 

1  Q 

26 

ISO 

122 

0.60 

0.6 

14.6 

83.5 

15-4 

IO.O 

27.0 

19.5 

72 

20 

3i 

27 

27 

123 

402 

0.47 

0.6 

14.9 

ii3-9 

15-7 

33-° 

21.4 

17-7 

83 

IO 

17 

16 

28 

212 

0.47 

0.6 

14.6 

105.0 

15-2 

18.3 

23.I 

17.7 

76 

20 

27 

23 

29 

116 

124 

0.47 

0.6 

14.6 

102.6 

15-0 

ii  .  i 

24.7 

i7-5 

7i 

25 

3i 

28 

30 

189 

406 

o-39 

0.6 

14.8 

135-4 

15-4 

36.3 

20.4 

16.3 

80 

12 

19 

18 

31 

124 

216 

0.39  !     0.6 

14.6 

124.0 

i5  6 

20.3 

21.3 

16.3 

77 

19 

26 

23 

32 

150 

131 

0.39        0.6 

14.6 

120.0 

15-0 

12.7 

23-7 

16.3 

69 

30 

33 

27 

passage  for  the  steam  to  and  from  the  cylinders.  The  dis- 
tribution of  steam  is  accomplished  by  three  single-acting 
piston-valves  on  one  continuous  valve-spindle  inside  the 
hollow  piston-rod.  The  ports  are  cut  through  the  side  of  the 
hollow  piston-rod  at  the  proper  places  above  and  below  each 
piston.  The  cut-off  is  produced  by  allowing  the  admission- 
port  to  run  into  the  packing-ring  in  the  cylinder-head  through 
which  the  piston-rod  works,  and  is  consequently  very  sharp. 


ECONOMY  OF  STEAM-ENGINES.  4°5 

TABLE   XLI. 

TESTS    ON    WILLANS    ENGINE,  COMPOUND    CONDENSING. 


Steam  per 

Point  of 
cut-off. 

Pressures,  pounds 
per  square  inch. 

lorse-power 
per  hour, 

Per  cent  of  water 
in  cylinder. 

pounds. 

W 

3 

4) 

V 

•a 

u 

3 

i 

i  , 

w       u 

j 

ii 

8 

1 

:§ 

c 

' 

* 

.    O 

o. 

r 

1    * 

c 

"O 

C 

1 

3 

u 

CJ 

u 

ti 

a 

«*      ">, 

>< 

•^ 

C 
1 

a 

en 

u 

? 

j3 

3 

1 

"o       °. 

o       a 

a 

u 
(i 

o 

a 

a 

.2 

rt 
u 

volutioi 

I 

a 

.c 
bt 

1 

rometer 

! 

O. 

1 

rt 

0 

1 

ll 

1 
c 

;:. 

.C 

I 

1 

i 

i 

1) 
£ 

E 

~ 

X 

H 

i 

1 

C 

u 

« 

£    u 

5 

3         V 

u  |  -2 

I 

i78 

402 

0.58 

0.45 

14.7 

134-7 

1  .1 

40.1 

16.7 

9-5 

57  1   TI 

IO 

28 

18 

2 

405 

0.58 

°-45 

14.7 

I.I 

33-2 

17.0 

9.8 

58  !   ii 

8 

28 

21 

3 

175 

4OI 

0.58 

0.45 

15.1 

90.1 

I.I 

25.6 

'7-3 

IO.I 

58  ,     9 

Q 

3° 

21 

4 

177 

404 

0.58 

0.45 

14.6 

64.6 

I    O 

18.7 

18.0 

10.4 

58         12 

10 

27 

17 

5 

151 

399 

0.58 

0-45 

14.6 

42.6 

I.O 

10.8 

20.3 

10.8 

53      12 

IO 

32 

15 

6 

137 

3Ji 

0.58 

0-45 

14.8 

134.8 

1  .0 

31.0 

16-3 

9-3 

57      " 

7 

29 

21 

7 

147 

3" 

0.58 

0-45 

14.6 

0.9 

25-7 

16.9 

92 

55  i   ir 

8 

30 

23 

8 

139 

301 

o.S8 

0-45 

14.5 

8q.S 

0.9 

19-5 

17.6 

9-7 

55  !   12 

9 

'4 

22 

9 

i84 

302 

0.58 

o-45 

15-2 

I.I 

14.0 

18.5 

10.3 

55   i   *3 

ii 

.36 

24 

10 

179 

300 

0.58 

0.45 

14.7 

39-7 

I.I 

7-9 

22.  O 

II.  2 

Si   !   17 

12 

40 

21 

ii 

121 

203 

0.58 

o-45 

14.6 

129.6 

0.9 

19.9 

I7.I 

8.6 

50    1    12 

IO 

38 

27 

12 

120 

198 

0.58 

o  45 

14.8 

89.8 

0.9 

13-3 

ig.O 

9.0 

48      18 

13 

45   i   3i 

13 

156 

203 

o.  58 

o-45 

14.7 

64.7 

I.O 

9-4 

20.1 

9-7 

48      18 

12 

46      33 

14 

I7I 

196 

0.58 

o-45 

14.8 

39-8 

1  .0 

5-3 

23-8 

10.9 

46      26 

16 

48   '   30 

IS 

I32 

US 

0.58 

o-45 

14.6 

119.6 

I.O 

9.0 

19.7 

8-3 

42       19 

16 

51       43 

16 

I94 

116 

0.58 

0-45 

14-8 

89.8      0.9 

6.7 

2O.  I 

8-7 

43 

21 

16 

Si 

37 

17 

170 

112 

0.58 

o-45 

14.8 

42.8 

I.I 

2.9 

27.0 

10.6 

39 

32 

24 

59 

39 

18 

123 

397 

0.28 

0-45 

14.6 

164.6 

o.g 

33-2 

14-8 

ii  .0 

S7 

26 

17 

32 

27 

19 

175 

399 

0.28 

o-45 

14-6 

139.6      i.o 

27.1 

15-2 

11.7 

S7 

23 

IS 

33 

25 

20 

171 

402 

o  28 

0-45 

14-7 

114.7         O.8          22.1 

15-8 

12.3 

ss 

22 

16 

38 

26 

21 

H4 

396 

0.28 

o-45 

14-8 

64  8      0.9 

11.7 

18.2 

12.4 

52 

32 

16 

45 

3° 

22 

155 

394 

0.28 

0.45 

14-9 

<55-9 

0.8 

11.9 

18.3 

13.1 

5i 

28 

15 

42 

27 

23 

l63 

296 

0.28 

o-45 

14.7 

139-7 

0.9 

22.1 

15.2 

10.9 

56 

28 

16 

.37 

28 

24 
25 

173 

166 

199 
118 

0.28 
0.28 

0.45 
0.45 

14-7 

14.8 

139-7 
163.8 

0.9 
0.9 

I4.8 

8.8 

16.5 

17.2 

11.4 
"•3 

}j 

34 

25 

48 
52 

39 
43 

26 

152 

402 

0.18 

0.45 

14.9 

174-9 

0.9 

27-5 

14-3 

9.9 

S8 

3i 

14 

36 

25 

27 

121 

398 

0.18 

0.45 

14.9 

139-9 

0.8 

21.6 

15.0 

10.3 

S6 

3i 

19 

37 

27 

28 

169 

407 

o.iS 

0-45 

15-0 

93-° 

o  8 

13.2 

17.2 

10.4 

Si 

40 

18 

44 

29 

157 

3°4 

0.18 

°-45 

15.1 

165.1 

0.7 

19.9  i  15.2 

9-7 

S2 

36 

16 

43 

33 

3<> 
31 
32 

i 

300 
203 
199 

0.18 
0.18 
0.18 

0-45 
o-45 
0-45 

15-2 
'52 
15-2 

93-2 
164.2 
80.2 

0.8 

I.O 

i  .0 

10.6 
'IS 

17.8 

i   16.8 
21-5 

II.  0 

9-7 
10.4 

49 
47 
42 

38 
42 

3 

23 

49 
48 
56 

33 
34 

211 

I58 

404 
396 

0.14 
0.14 

o-45 
0-45 

14.7 
14.6 

186.7 
119.6 

1.2 

I  .O 

24.9 
16.0 

14.7 
15-5 

9-2 

9-4 

57 
57 

37 
39 

16 

23 

35 
39 

26 
29 

406 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


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Per  cent  of  water  in  cylinder. 

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Non-condensing  •{  4 

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Condensing  —  •<  13 
(  14 

u 
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i 

ECONOMY  OF  STEAM-ENGINES.  407 

Steam  is  admitted  to  the  upper  sides  of  the  pistons  and  ex- 
hausted on  the  down  stroke;  on  the  up  stroke  the  steam  is 
transferred  to  the  under  sides  of  the  pistons.  The  spaces 
below  the  high-pressure  and  intermediate  pistons  have  con- 
siderable volume  and  serve  as  receiver-spaces;  but,  as  the 
volumes  of  these  spaces  increase  during  the  up  stroke  and  as 
work  is  done  on  the  under  side  of  the  pistons  on  that  stroke, 
each  receiver-space  gives  an  intermediate  expansion,  and  there 
are  in  reality  five  stages  of  expansion  for  the  triple  engine. 
To  insure  a  downward  thrust  at  all  times  on  the  connecting- 
rod,  an  air-cushion  is  provided  at  the  lower  end  of  the  hollow 
piston-rod.  For  this  purpose,  and  also  to  provide  a  guide  for 
the  lower  end  of  the  piston-rod,  there  is  a  trunk  or  plunger 
working  in  a  cylinder  which  is  closed  at  the  top  and  filled 
with  air  that  is  always  at  a  pressure  somewhat  greater  than 
that  of  the  atmosphere;  on  the  up  stroke  this  air  is  com- 
pressed and  it  expands  again  on  the  down  stroke. 

Two  or  three  of  these  engines  are  placed  side  by  side  on 
the  same  bed;  two  engines  with  their  cranks  opposite  are 
equivalent  to  an  ordinary  double-acting  engine;  three  engines 
with  their  cranks  at  120°  form  a  very  smoothly  running  com- 
bination. 

Mr.  Willans  first  made  tests  in  1887  on  one  of  his  engines 
which  was  designed  to  run  without  condensation,  and  four 
years  later  made  further  tests  on  a  condensing-engine  which 
had  somewhat  different  proportions,  to  accord  with  the  greater 
range  of  pressures  and  temperatures  available  with  a  vacuum. 
The  dimensions  of  these  engines  are  as  follows: 

Non-condensing.  Condensing. 

Diameters,  inches  : 

High-pressure  cylinder 7  6 

Intermediate  cylinder 10  8.5 

Low-pressure  cylinder 14  14 

Stroke,  inches 6  6 

One  single-acting  engine  was  used  for  the  tests  in  both 
cases  to  make  the  work  simpler  and  easier;  two  or  three 
engines  running  in  combination  would  of  course  do  two  or 


408  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

three  times  as  much  work  and  use  two  or  three  times  as  much 
steam.  During  the  tests  the  speed  of  the  engine  was  limited 
to  400  revolutions  per  minute  for  the  sake  of  getting  clearer 
indicator-diagrams;  in  practice  the  engines  tested  run  at  500 
revolutions  per  minute. 

In  the  tests  on  the  non-condensing  engine  the  steam  was 
drawn  from  a  special  boiler,  and  the  steam-consumption  was 
determined  by  weighing  the  feed-water,  special  precautions 
being  taken  to  have  the  water-level  and  the  rate  of  vaporiza- 
tion in  the  boiler  the  same  at  the  beginning  and  end  of  a 
test;  Mr.  Willans  estimated  the  error  in  the  determination  of 
the  steam  used  for  a  test  at  one  fourth  of  one  per  cent. 
During  the  tests  on  the  condensing  engine  steam  was  drawn 
from  a  general  supply,  and  the  exhaust-steam  was  condensed 
in  a  surface-condenser,  and  was  collected  and  weighed  in  a 
closed  tank  to  avoid  surface  evaporation.  In  both  cases  the 
steam  was  found,  by  proper  tests,  to  be  dry  and  saturated 
near  the  engine. 

By  removing  the  upper  piston  and  supplying  steam  to  the 
intermediate  cylinder  directly,  the  engine  was  run  as  a  com- 
pound engine;  but  as  the  steam  was  transferred  to  the  space 
under  the  piston  and  did  work  on  it  before  going  to  the  low- 
pressure  cylinder,  the  engine  when  running  compound  had 
really  three  stages  of  expansion.  Again,  by  removing  the 
two  upper  pistons  the  engine  was  run  as  a  simple  engine. 

The  only  quantities  in  the  table  which  require  explanation 
jare  those  in  the  columns  headed  Steam  per  horse-power  per 
hour  required  by  a  perfect  engine  and  Percentage  of  efficiency. 
The  first  was  calculated  by  a  method  which  is  nearly  equiva- 
lent to  that  given  on  page  235,  and  the  efficiency  is  calculated 
by  dividing  the  steam-'consumption  for  a  non-conducting 
engine  by  the  actual  steam-consumption.  Since  all  the  steam 
passed  through  the  cylinders  of  the  engine,  this  method  is 
proper  for  this  engine.  The  per  cent  of  water  in  the  cylinder 
is  a  rough  index  of  the  extent  of  the  influence  of  the  walls  of 
the  cylinder. 


ECONOMY  OF  STEAM-ENGINES.  409 

Compounding. — The  most  efficacious  method  which  has 
been  devised  to  increase  the  amount  of  expansion  of  steam 
in  an  engine,  and  at  the  same  time  to  avoid  excessive  cylinder- 
condensation,  is  compounding;  that  is,  passing  the  steam  in 
succession  through  two  or  more  cylinders  of  increasing  size. 
An  engine  with  two  cylinders,  a  small  or  high-pressure 
cylinder  and  a  large  or  low-pressure  cylinder,  is  called  a 
compound  engine.  An  engine  with  three  cylinders,  a  high- 
pressure  cylinder,  an  intermediate  cylinder,  and  a  low-pressure 
cylinder,  is  called  a  triple-expansion  engine.  A  quadruple 
engine  has  a  high-pressure  cylinder,  a  first  and  a  second  inter- 
mediate cylinder,  and  a  low-pressure  cylinder.  Any  cylinder 
of  a  compound  or  multiple-expansion  engine  may  be  dupli- 
cated, that  is,  may  be  replaced  by  two  cylinders  which  are 
usually  of  the  same  size.  Thus,  at  one  time  a  compound 
engine  with  one  high-pressure  and  two  low-pressure  cylinders 
was  much  used  for  large  steamships.  Many  triple  engines 
have  two  low-pressure  cylinders,  which  with  the  high-pressure 
and  the  intermediate  cylinders  make  four  in  all.  Again,  some 
triple  engines  have  two  high-pressure  cylinders  and  two  low- 
pressure  cylinders  and  one  intermediate  cylinder,  making  five 
in  all. 

Two  main  questions  are  presented  for  investigation:  (i) 
under  what  conditions  should  compounding  be  resorted  to, 
and  (2)  how  much  gain  may  be  expected  ?  The  answer  to 
either  question  will  be  modified  by  the  type  of  engine  consid- 
ered, and  in  only  a  few  cases  can  explicit  conclusions  be 
drawn.  The  most  complete  investigation  of  these  questions 
is  that  by  Mr.  Willans;  our  only  regret  is  that  we  must  hesi- 
tate to  apply  conclusions  from  tests  on  so  small  and  so 
peculiar  an  engine  to  large  engines  of  more  common  construc- 
tion. And  yet  the  good  economy  shown  by  his  engine  under 
all  conditions  gives  an  importance  to  the  conclusions  from  his 
tests  which  can  seldom  be  attributed  to  tests  on  small  engines. 

Taking  first  the  tests  on  the  non-condensing  Willans 
engine,  we  may  compare  the  first  seven  tests  in  Table 


410  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

XXXVIII,  the  first  sixteen  in  Table  XL,  and  the  first  seven 
in  Table  XLII,  to  determine  the  advantage  of  using  a  com- 
pound or  a  triple-expansion  engine,  without  a  vacuum. 
Mr.  Willans  chose  the  number  of  expansions  (and  the  cut-off 
for  the  cylinder  taking  steam  from  the  boiler)  by  a  quasi- 
theoretical  method,  which  is  too  intricate  to  be  given  here. 
It  is  enough  to  say  that  it  gave  a  terminal  pressure,  in  the 
cylinder  exhausting  into  the  atmosphere,  of  about  five  pounds 
above  the  atmosphere.  One  series  of  tests,  namely,  17  to  23, 
Table  XL,  gives  direct  evidence  on  this  matter,  and  shows 
that  for  a  boiler-pressure  of  135  pounds  the  cut-off  may  be 
varied  from  0.31  to  0.43  of  the  stroke  of  the  high-pressure 
cylinder  without  serious  effect  on  the  economy.  For  the  re- 
mainder of  the  tests  on  the  non-condensing  engine  we  have 
no  other  direct  evidence  regarding  the  effect  of  cut-off,  than 
the  fact  that  the  steam-consumption  for  any  test  is  as  good 
as  the  conditions  would  lead  us  to  expect  for  an  engine  of 
the  size,  and  in  general  the  results  are  surprisingly  good. 

The  results  of  tests  on  the  non-condensing  engine,  when 
running  simple  or  compound,  are  plotted  on  Fig.  82,  using 
the  absolute  boiler-pressure  for  abscissae  and  the  steam-con- 
sumption for  ordinates.  The  results  of  tests  on  the  engine 
when  running  triple-expanding  are  not  plotted  on  the  diagram 
to  avoid  confusion,  and  because  it  does  not  appear  necessary. 
The  curve  for  compound  tests  is  well  located  and  shows  con- 
clusively that  little  if  any  gain  is  to  be  expected  from  increas- 
ing the  boiler-pressure  above  180  pounds;  indeed  it  appears 
wise  to  limit  the  pressure  to  165  pounds  absolute  or  150 
pounds  above  the  atmosphere.  An  inspection  of  the  results  of 
tests  i  to  7  of  Table  XLII  shows  that  there  is  no  advantage 
in  increasing  the  boiler-pressure  for  the  non-condensing  triple 
engine  above  185  pounds  absolute  or  170  pounds  above  the 
atmosphere.  Neither  the  results  of  tests  in  Table  XXXVIII 
nor  the  curve  on  Fig.  82  show  conclusively  the  maximum 
economical  steam-pressure  for  simple  engines,  but  it  is  doubt- 
ful whether  there  is  any  real  advantage  in  raising  the  steam- 


ECONOMY  OF  STEAM-ENGINES. 


411 


pressure  above  125  pounds  absolute  or  no  pounds  above  the 
atmosphere.  These  limits  of  1 10  pounds  for  a  simple  engine, 
150  pounds  for  a  compound  engine,  and  170  pounds  for  a 
triple  engine  can  apply  only  to  non-condensing  engines  and 


120  140 

FIG.  82. 

should   be   restricted   to   engines  of  the  Willans  type   or   of 
similar  types. 

To  determine  the  gain  from  compounding  we  may  con- 
sider that  the  steam-consumption  for  the  simple  engine  is  27 
pounds  per  horse-power  per  hour  with  a  boiler-pressure  of  125 
pounds  absolute,  that  the  consumption  for  the  compound 
engine  is  19.5  pounds  for  a  boiler-pressure  of  165  pounds 


412  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

absolute,  and  that  the  consumption  for  the  triple  engine  is 
^8.5  pounds  for  a  boiler- pressure  of  185  pounds  absolute. 
The  gain  from  compounding  is  therefore 

27  —  10.5 

-  X  ioo  =  28  per  cent. 

The  gain  from  using  the  triple  engine  instead  of  the  com- 
pound engine  is 

10.5  —  18.5 

— -  X   ioo  =  5  per  cent. 

Coming  now  to  Mr.  Willans'  tests  on  his  condensing 
engine,  we  find  that  for  each  arrangement  of  the  engine 
(simple,  compound,  and  triple)  he  made  several  series  of  tests 
with  constant  cut-off  and  varying  steam-pressure  for  each 
series.  Two  such  series  were  made  for  both  the  simple  and 
the  triple  engine  when  running  at  full  speed,  and  four  series 
at  full  speed  were  made  for  the  compound  engine. 

As  has  already  been  pointed  out,  the  series  of  simple  tests 
with  the  cut-off  at  0.5  of  the  stroke  showed  no  advantage  in 
raising  the  pressure  beyond  55  pounds  absolute;  the  series 
with  the  cut-off  at  0.29  of  the  stroke  showed  that  the  steam- 
pressure  could  be  advantageously  raised  to  at  least  85  pounds 
absolute,  and  under  these  conditions  the  steam-consumption 
of  22.2  pounds  per  horse-power  per  hour  was  probably  a 
minimum. 

The  engine  running  compound-condensing  gives  its  best 
economy  (14.3  pounds  of  steam  per  horse-power  per  hour) 
when  running  at  full  speed  with  175  pounds  absolute  steam- 
pressure,  and  with  the  cut-off  for  the  high-pressure  cylinder  at 
o.i  8  of  the  stroke,  but  nearly  as  good  results  are  attained  for 
a  cut-off  at  o.  14  and  for  a  cut-off  at  0.28  of  the  stroke.  The 
two  series  for  the  triple  engine  with  the  cut-off  for  the  high- 
pressure  cylinder  at  0.3  and  at  0.5  of  the  stroke  show  the 
same  economy  of  12.7  pounds  of  steam  per  horse-power  per 
hour  with  the  steam-pressure  of  185  pounds  absolute. 


ECONOMY  OF  STEAM-ENGINES.  413 

The  gain  from  compounding  is  therefore 

22.2  —   14.3 


22.2 


X   ioo  =  35  per  cent; 


and  the  gain  from  using  a  triple  instead  of  a  compound  engine 
is 

14.3-  12.7 


14-3 


X  ioo  =  1 1  per  cent. 


It  is  very  interesting  to  consider  the  effect  of  the  increase 
of  steam-pressure  on  the  percentage  of  efficiency  of  the  engine 
in  these  tests  on  Mr.  Willans'  engine.  This  percentage  is 
greater  for  the  non-condensing  than  for  the  condensing  engine, 
and  is  in  general  greater  for  low  than  for  high  pressure,  which 
can  readily  be  accounted  for  by  the  greater  initial  condensa- 
tion and  re-evaporation  accompanying  a  wider  range  of  pressure 
and  temperature.  It  is,  however,  notable  that  the  compound 
and  triple  engines  maintain  the  efficiency  better  than  the 
simple  engine  does,  and  that  the  percentage  of  efficiency  is 
high  for  those  engines  at  all  pressures.  The  non-condensing 
engine  shows  about  the  same  ratio  of  efficiency  when  running 
compound  and  when  running  triple;  but  the  condensing 
engine  has  a  decided  advantage  in  this  regard  when  running 
triple.  This  agrees  very  well  with  the  fact  that  there  is  a 
gain  of  1 1  per  cent  for  the  condensing  engine,  and  only  5  per 
cent  for  the  non-condensing  engine,  to  be  attained  by  running 
triple  instead  of  compound. 

The  tests  on  this  engine  at  reduced  speeds  will  be  referred 
to  later. 

Gain  from  Compounding. — In  considering  the  gain  to  be 
attained  by  compounding,  it  has  sometimes  been  considered 
that  the  engines  compared  should  have  the  same  steam- 
pressure,  in  order  that  the  comparison  should  be  fair  to  the 
simple  engine;  and  a  similar  condition  has  been  claimed  for 
comparisons  of  compound  and  triple  engines.  But  the  object 
of  compounding  is  the  ability  to  use  high  pressures  and  large 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


ratios  of  expansion  to  advantage.  Each  engine  should  there- 
fore be  run  under  its  best  condition,  using  as  high  a  pressure 
and  as  large  an  expansion  as  may  be  profitable.  Of  course 
each  engine  should  have  the  advantage  of  using  steam-jackets 
or  superheated  steam,  or  else  both  should  be  without  these 
aids.  In  general,  comparisons  should  be  made  only  between 
engines  which  show  a  good  economy  for  their  respective 
types. 

Let  us  take  for  example  tests  on  the  experimental  engine 
at  Cornell  University  using  all  three  cylinders  to  form  a  triple 
engine,  the  two  smaller  cylinders  to  form  a  compound  engine, 
or  the  small  cylinder  as  a  simple  engine. 

CORNELL    EXPERIMENTAL    ENGINE. 


Data  and  Results. 

Simple. 

Compound. 

Triple. 

Revolutions  per  minute  . 

Re  A 

Re    A 

0  -     _ 

Steam-pressure  above  atmosphere  

°5-4 

°5-4 

05-° 

TT  f\     T 

Total  expansion  

97-7 

95-4 

Steam  per  horse-power  per  hour,  pounds.  .  .  . 
B  T   U   per  horse-power  per  minute.  .  . 

•9 
23.1 

I2-5 
16.3 

OK  A 

21.9 
13-7 

411 

237 

It  is  probable  that  the  simple  engine  has  too  high  steam- 
pressure  and  the  triple  engine  has  too  low  pressure.  How- 
ever, making  comparisons  as  the  results  stand,  we  have  as  the 
gain  from  compounding 

284 

100  =31  per  cent, 


411 


411 


X 


and  from  using  a  triple  instead  of  a  compound  engine 
284-  237 


284 


X  ioo  =  20  per  cent. 


On  the  other  hand,  a  comparison  of  the  results  of  tests  on 
the  engines  of  the  Rusk  and  the  Gallatin  (Table  XXXII, 
page  388,  tests  18  and  36)  shows  a  gain  of  only 

20.5  —  18.4 


20.5 


X  ioo  =  10  per  cent; 


ECONOMY  OF  STEAM-ENGINES. 


415 


but  it  is  very  clear  that  the  steam-pressure  and  the  expansion 
are  too  small  for  the  best  economy  of  a  compound  engine. 
And  again,  while  the  Gallatin  shows  a  fair  economy  for  a 
simple  engine,  the  economy  of  the  Rush  is  poor. 

Taking  now  the  best  results  of  tests  on  simple,  compound, 
and  triple  engines  from  Table  X,  all  being  supplied  with 
steam-jackets,  and  the  compound  and  triple  engines  with 
intermediate  reheaters,  we  have  the  following  results : 


Data  and  Results. 

Simple 
Corliss  at 
Creusot. 

Compound 
Leavitt  at 
Louisville. 

Triple 
Leavitt  at 
Chestnut 
Hill. 

60 

18  6 

50  6 

Steam-pressure  above  atmosphere,  pounds.  .. 

84 

137 
2O 

176 

21 

Steam  per  horse-power  per  hour,  pounds.  .  .  . 
B   T    U    per  horse-power  per  minute.  •  •  . 

16.9 

12.2 
222 

II.  2 
2O4 

Using  the  steam-consumption  as  the  basis  of  comparison, 
we  have  for  the  gain  from  compounding 

16.9  —  12.2 


16.9 


X  100  =  28  per  cent; 


and  for  the  gain  from  using  a  triple  instead  of  a  compound 
engine 

12.2  —  1 1.2 


12.2 


X  ioo  =  8  per  cent. 


The  total  expansion  for  the  two  Leavitt  engines  is  nearly 
the  same,  but  is  obtained  by  different  means.  The  ratio  of  the 
large  to  the  small  cylinder  of  the  compound  engine  is  a  trifle 
less  than  four,  and  the  cut-off  for  the  high-pressure  cylinder 
is  a  little  less  than  one-fifth  stroke.  The  triple  engine  has  a 
little  more  than  eight  for  the  extreme  ratio  of  the  cylinders, 
and  has  the  cut-off  for  the  high-pressure  cylinder  at  a  little 
more  than  four  tenths.  In  the  design  of  a  compound  engine 
the  desired  expansion  may  be  attained  either  by  using  a  small 
ratio  'for  the  cylinders  and  a  short  cut-off  for  the  high-pressure 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

cylinder,  or  by  using  a  large  ratio  for  the  cylinders  and  a  long 
cut-off  on  the  high-pressure  cylinder.  The  compound  pump- 
ing-engine  at  Louisville  now  under  discussion  was  designed 
by  the  first  method,  giving  remarkable  results.  Some  de- 
signers have,  on  the  other  hand,  claimed  an  exceptional  econ- 
omy for  certain  compound  engines  which  have  a  large  ratio  of 
large  to  small  cylinders,  and  have  preferred  them  to  triple 
engines.  In  confirmation  we  have  the  results  of  tests  in 
Table  XX,  page  362,  on  an  engine  which  was  run  triple,  using 
three  cylinders,  and  compound,  using  only  the  large  and  small 
cylinders,  omitting  the  intermediate  cylinder.  These  tests 
show  as  good  an  economy  for  the  compound  engine  as  for  the 
triple  engine,  and  tests  given  in  Table  XXIII  on  an  engine 
with  a  larger  ratio  of  cylinders  and  a  very  large  total  expan- 
sion show  even  better  economy.  But  the  result  (13  pounds 
of  steam  per  horse-power  per  hour),  though  good,  is  not 
so  low  as  that  for  the  Louisville  engine,  and  is  but  little 
better  than  is  given  in  Table  XIX  for  a  compound  mill-engine 
at  New  Bedford,  which  has  a  moderate  ratio  of  cylinders  and 
much  smaller  expansion.  The  New  Bedford  engine  was  sup- 
plied with  slightly  superheated  steam,  but  had  no  steam- 
jackets.  Finally  the  indicator  diagrams  from  the  high-pressure 
cylinder  of  the  Holyoke  engine  (Table  XX)  when  running 
triple  showed  clearly  that  the  cut-off  for  the  intermediate 
cylinder  was  too  short  and  the  back-pressure  for  the  high- 
pressure  cylinder  was  too  high,  because  the  expansion  line 
reached  the  back-pressure  line  at  about  two-thirds  stroke.  It 
cannot  therefore  be  determined  which  method  of  obtaining 
the  desired  expansion  for  a  compound  engine  is  the  better. 

Marine  engines  will  not  run  smoothly  with  a  short  cut-off, 
and  consequently  a  large  number  of  expansions  can  be 
obtained  only  by  using  a  large  ratio  of  cylinders.  But  even 
for  triple  engines  the  ratio  of  the  large  to  the  small  cylinder 
is  commonly  five  or  six  and  the  total  expansions  are  corre- 
spondingly small.  The  advantage  of  using  a  larger  ratio, 
when  allowable,  is  shown  by  comparing  the  tests  in  Table 


ECONOMY   OF  STEAM-ENGINES.  417 

XIV,  page  358,  on  the  Meteor  and  on  the  lona ;  the  engine 
of  the  lona  had  the  further  advantage  of  higher  steam-pressure 
and  a  relatively  early  cut-off  on  the  high-pressure  cylinder. 

In  conclusion,  it  may  be  said  that  for  condensing  engines 
there  is  no  advantage  in  using  more  than  80  pounds  steam- 
pressure,  while  compound  engines  may  advantageously  have 
the  pressure  raised  to  135  pounds  above  the  atmosphere. 
The  gain  from  higher  steam-pressure  and  compounding  will 
be  25  to  30  per  cent.  The  best  pressure  for  triple  engines 
cannot  now  be  determined  from  experiments;  it  is,  however, 
doubtful  if  there  is  any  advantage  in  using  more  than  17$ 
pounds  above  the  atmosphere.  Such  a  further  increase  of 
pressure  and  the  use  of  a  triple  instead  of  a  compound  engine 
may  be  expected  to  give  8  or  10  per  cent  better  economy. 

For  a  simple  non-condensing  engine  the  steam-pressure 
may  be  100  to  115  pounds  above  the  atmosphere,  and  for  a 
compound  engine  the  pressure  may  be  150  pounds,  while  for 
a  triple  engine  the  pressure  may  be  175  pounds  or  possibly 
somewhat  more.  The  gain  from  compounding  will  be  20  to 
30  per  cent,  and  the  gain  from  using  a  triple  instead  of  a 
compound  engine  will  be  5  per  cent  or  perhaps  a  little  more. 

These  conclusions  apply  only  when  the  engine  is  run  at 
full  power  and  at  the  best  point  of  cut-off  or  the  most 
economical  total  expansion.  In  general  the  compound  engine 
will  suffer  more  loss  of  economy  when  running  at  a  reduced 
load  than  a  simple  engine  will;  and  a  triple  engine  will  suffer 
even  more  than  a  compound  engine  from  the  same  cause. 

Cut-off  and  Expansion. — It  has  already  been  pointed  out 
on  page  385  in  connection  with  Delafond's  tests  that  the  best 
point  of  cut-off  for  a  simple  engine,  whether  jacketed  or  not, 
is  about  one-third  stroke  when  the  engine  is  non-condensing 
and  it  is  about  one-sixth  stroke  when  condensing.  In  general, 
other  tests  on  simple  engines  such  as  those  on  the  Bacher 
Dexter,  and  Gallatin  (Table  XXXII,  page  388),  and  on  the 
small  Corliss  engine  at  the  Massachusetts  Institute  of  Tech- 
nology (Tables  II  and  XXVII,  pages  318  and  371),  confirm. 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

these  conclusions.  Tests  on  the  experimental  engine  at 
Cornell  (Table  XXXVI,  page  397)  indicate  that  a  longer  cut- 
off than  one-sixth  may  be  used  to  advantage,  but  these  tests 
were  made  with  a  poor  vacuum  and  consequently  show  a  poor 
economy  for  all  grades  of  cut-off. 

The  term  total  expansion  for  a  compound  or  a  triple 
engine  can  properly  have  only  a  conventional  significance;  it 
is  usually  taken  to  be  the  product  of  the  ratio  of  the  large  to 
the  small  cylinder  by  the  reciprocal  of  the  fraction  of  the 
stroke  at  cut-off  for  the  high-pressure  cylinder.  This  conven- 
tional total  expansion  is  about  20  for  all  the  tests  on  triple 
engines  quoted  in  Table  X,  page  354,  except  those  on  marine 
engines,  which  show  a  relatively  poor  economy.  It  may  there- 
fore be  concluded  that  it  is  not  advisable  to  use  much  more 
expansion  for  any  triple  engine,  and  that  less  expansion 
should  be  used  only  when  the  conditions  of  service  (for  exam- 
ple, at  sea)  prevent  the  use  of  large  expansion. 

The  case  is  not  so  clear  for  compound  engines.  The 
Louisville  engine,  which  gives  the  best  economy  of  any  com- 
pound engine  quoted  in  Table  X,  has  20  expansions.  The 
Natick  engine  has  33  expansions,  which  are  clearly  excessive, 
and  the  engine  at  New  Bedford  (page  361)  has  only  13.4. 
The  Cornell  engine  (page  397)  gives  its  best  economy  when 
running  compound  with  12  or  16  expansions.  We  may  con- 
clude that  in  general  15  expansions  may  be  used  to  advantage; 
marine  engines  and  other  engines  which  cannot  readily  be 
designed  for  so  much  expansion  may  be  expected  to  give  a 
less  economy  in  consequence. 

Variation  of  Load. — In  general  an  engine  should  be  so 
designed  that  it  may  give  a  fair  economy  for  a  considerable 
range  of  load  or  power.  Very  commonly  the  engine  will  have 
sufficient  range  of  power  with  good  economy  if  designed  to  give 
the  best  economy  at  the  normal  load.  In  general,  however, 
it  is  well  to  assign  a  less  expansion  and  consequently  a  longer 
cut-off  to  the  engine  than  would  be  determined  from  a  con- 
sideration of  the  steam-  (or  heat-)  consumption  alone.  For, 


ECONOMY   OF  STEAM-ENGINES.  419 

in  the  first  place,  the  best  brake  or  dynamic  economy  is  always 
attained  for  a  little  longer  cut-off  than  that  which  gives  the 
best  indicated  economy,  and  in  the  second  place  the  econ- 
omy is  less  affected  by  lengthening  than  by  shortening  the 
cut-off.  The  first  comes  from  the  fact  that  the  frictional 
losses  of  the  engine  increase  less  rapidly  than  the  power,  as 
will  be  shown  in  the  next  chapter;  and  the  second  is  evident 
from  consideration  of  curves  of  steam-consumption  as  given 
by  Fig.  8 1,  page  390,  and  Figs.  79  and  80,  pages  383-4. 

The  allowable  range  of  power  for  a  simple  engine  is  greater 
than  for  a  compound  or  a  triple  engine.  Comparisons  for  a 
simple  and  a  triple  engine  may  be  made  by  aid  of  Figs. 
80  and  81.  The  Corliss  engine  at  Creusot  when  supplied 
with  steam  at  60  pounds  pressure,  with  condensation  and  with 
steam  in  the  jacket,  developed  150  horse-power  and  used  17.3 
pounds  of  steam  per  horse-power  per  hour.  If  the  increase 
be  limited  to  10  per  cent  of  the  best  economy,  that  is,  to  19 
pounds  per  horse-power  per  hour,  the  horse-power  may  be 
reduced  to  about  92,  giying  a  reduction  of  nearly  40  per  cent 
from  the  normal  power.  The  triple  engine  at  the  Massa- 
chusetts Institute  of  Technology  with  steam  at  150  pounds 
pressure  and  using  steam  in  all  the  cylinder-jackets  developed 
140  horse-power  and  used  233  B.  T.  U.  per  horse-power  per 
minute.  Again,  limiting  the  increased  consumption  to  10  per 
cent  or  to  254  B.  T.  U.,  the  power  may  be  reduced  to  about 
104  horse-power,  giving  a  reduction  of  26  per  cent  from  the 
normal  power.  The  effect  of  increasing  power  for  these 
engines  cannot  be  well  shown  from  the  tests  made  on  them, 
but  there  is  reason  to  believe  that  the  simple  engine  would 
preserve  its  advantage  if  a  comparison  could  be  made. 
Though  the  tests  which  we  have  on  compound  engines  do  not 
allow  us  to  make  a  similar  investigation  of  the  effect  of 
changing  load,  there  is  no  doubt  that  it  is  intermediate  in  this 
respect  between  the  simple  and  the  triple  engine. 

When   the   power   developed    by   a   compound    engine   is 
reduced  by  shortening  the  cut-off  of  the  high-pressure  cylin- 


420  THERMODYNAMICS    OF    THE   STEAM-ENGINE. 

der,  the  cut-off  of  the  low-pressure  cylinder  must  be  shortened 
at  the  same  time  to  preserve  a  proper  distribution  of  power 
and  division  of  the  range  of  temperature  between  the  cylin- 
ders. If  this  is  not  done  the  work  will  be  developed  mainly 
in  the  high-pressure  cylinder,  which  will  be  subjected  to  a 
large  fluctuation  of  temperature,  and  the  engine  will  lose  the 
advantages  sought  from  compounding.  A  compound  non- 
condensing  engine,  if  the  cut-off  for  the  large  cylinder  is  fixed, 
is  likely  to  have  a  loop  on  the  low-pressure  indicator-diagram 
due  to  expansion  below  the  atmosphere,  if  the  power  is 
reduced  by  shortening  the  cut-off  of  the  high-pressure  cyl- 
inder. Such  a  loop  is  always  accompanied  by  a  large  loss  of 
economy;  if  the  loop  is  large  the  engine  may  be  more  waste- 
ful than  a  simple  engine,  for  the  high-pressure  piston  develops 
nearly  all  the  power  and  may  have  to  drag  the  low-pressure 
piston,  which  is  then  worse  than  useless. 

There  is  seldom  much  difficulty  in  running  a  simple  engine 
at  any  desired  reduced  power  by  shortening  the  cut-off  or 
reducing  the  steam-pressure,  or  by  a. combination  of  the  two 
methods.  But  a  compound  engine  sometimes  gives  trouble 
when  run  at  very  low  power  (even  when  attention  is  given  to 
the  cut-off  of  the  low-pressure  cylinder),  which  usually  takes 
the  form  just  discussed;  i.e.,  the  power  is  developed  mainly 
in  the  high-pressure  cylinder.  Triple  engines  are  even  more 
troublesome  in  this  way.  A  compound  or  triple  engine 
running  at  much  reduced  power  is  subject  not  only  to  loss  of 
economy  and  to  irregular  action,  but  the  inside  surface  of  the 
low-pressure  cylinder  is  liable  to  be  cut  or  abraded. 

Automatic  and  Throttle  Engines. — The  power  of  an 
engine  may  be  regulated  by  (i)  controlling  the  steam-pressure 
or  (2)  by  adjusting  the  cut-off.  Usually  these  two  methods 
are  used  separately,  but  in  some  instances  they  are  used  in 
combination.  Thus  a  locomotive-driver  may  reduce  the  pov/er 
of  his  engine  either  by  shortening  the  "cut-off  or  by  partially 
closing  the  throttle-valve,  or  he  may  do  both  at  once.  Sta- 
tionary engines  are  usually  run  at  a  fixed  speed  and  are  con- 


ECONOMY   OF  STEAM-ENGINES.  421 

trolled  by  mechanical  governors,  which  commonly  consist  of 
revolving  weights  that  are  urged  away  from  the  axis  of  revo- 
lution by  centrifugal  force  and  are  restrained  by  the  attrac- 
tion of  gravity  or  by  the  tension  of  springs. 

The  earliest  and  simplest  steam-engine  governor,  invented 
by  Watt,  has  a  pair  of  revolving  pendulums  (balls  on  the  ends 
of  rods  that  are  hinged  to  a  vertical  spindle  at  their  upper 
ends)  which  are  urged  out  by  centrifugal  force  and  are  drawn 
down  by  gravity.  When  the  engine  is  running  steadily  at  a 
given  speed  the  forces  acting  on  the  governor  are  in  equilib- 
rium and  the  balls  revolve  in  a  certain  horizontal  plane.  If 
the  load  on  the  engine  is  reduced  the  engine  speeds  up  and  the 
balls  move  outward  and  upward  until  a  new  position  of  equili- 
brium is  found  with  the  balls  revolving  in  a  higher  horizontal 
plane.  Through  a  proper  system  of  links  and  levers  the  up- 
ward motion  of  the  balls  is  made  to  partially  close  a  throttle- 
valve  in  the  pipe  which  supplies  steam  to  the  engine  and  thus 
adjusts  the  work  of  the  engine  to  the  load. 

Shaft-governors  have  large  revolving-weights  whose  centri- 
fugal forces  are  balanced  by  strong  springs.  They  are  powerful 
enough  to  control  the  distribution  or  the  cut-off  valve  of  the 
engine,  which,  however,  must  be  balanced  so  that  it  may  move 
easily. 

Automatic  engines,  like  the  Corliss  engines,  have  four 
valves,  two  for  admission  and  two  for  exhaust  of  steam.  The 
admission,  release,  and  compression  are  fixed,  but  the  cut-off 
is  controlled  by  the  governor.  Usually  an  admission-valve  is 
attached  to  the  actuating  mechanism  by  a  latch  or  similar 
device,  which  can  be  opened  by  the  governor,  and  then  the 
valve  is  closed  by  gravity,  by  a  spring,  or  by  some  other  inde- 
pendent device.  The  office  of  the  governor  is  to  control  the 
position  of  a  stop  against  which  the  latch  strikes  and  by  which 
it  is  opened  to  release  the  valve. 

Corliss  and  other  automatic  engines  have  long  had  a 
deserved  reputation  for  economy,  which  is  commonly  attribu- 


422  THERMODYNAMICS  OF   THE   STEAM-ENGINE* 

ted  to  their  method  of  regulation.  It  is  true  that  the  valve- 
gears  of  such  engines  are  adapted  to  give  an  early  cut-off,  which 
is  one  of  the  elements  of  the  design  of  an  economical  simple 
engine,  but  their  advantage  over  some  other  engines  is  to  be 
largely  attributed  to  the  small  clearance  which  the  use  of  four 
valves  makes  convenient,  and  to  the  fact  that  the  exhaust- 
steam  is  led  immediately  away  from  the  engine,  without  hav- 
ing a  chance  to  abstract  heat  after  it  leaves  the  cylinder. 
These  engines  also  are  free  from  the  loss  which  Callendar  and 
Nicolson  attribute  to  direct  leakage  from  the  steam  to  the  ex- 
haust side  of  slide-valves,  and  to  valves  of  similar  construction. 
And  yet  the  Hoadley  engine  (Table  XXII,  page  363),  which 
was  of  the  second  type  having  a  piston-valve  controlled  by  a 
shaft-governor,  compares  very  favorably  with  the  Corliss  en- 
gine at  Creusot  (Table  XXXI,  page  382),  though  it  must  be 
admitted  that  the  performance  of  the  Hoadley  engine  is 
exceptionally  good  for  its  type. 

Every  steam-engine  should  have  a  reserve  of  power  in  ex- 
cess of  its  normal  power;  and  again  it  is  convenient  if  not 
essential  that  a  single-cylinder  engine  should  be  able  to  carry 
steam  through  the  greater  part  of  its  stroke  in  starting. 
These  conditions,  together  with  the  fact  that  it  is  somewhat 
difficult  to  design  a  plain  slide-valve  engine  to  give  an  early 
cut-off,  have  led  to  the  use  of  a  long  cut  off  for  engines  con- 
trolled by  a  throttle-governor.  The  tests  on  the  Corliss  en- 
gine at  Creusot  (Tables  XXX  and  XXXI,  pp.  381  and  382) 
show  clearly  the  disadvantage  of  using  a  long  cut-off  for  sim- 
ple engines.  It  has  already  been  pointed  out  that  a  non-con- 
densing engine  should  have  the  cut-off  at  about  one-third 
stroke.  With  cut-off  at  that  point  and  with  75  Ibs.  steam- 
pressure  the  engine  developed  209  horse-power  and  used  24.2 
Ibs.  of  steam  per  horse-power  per  hour  when  running  without 
steam  in  the  jacket  and  without  condensation.  If  the  steam- 
pressure  is  reduced  to  50  Ibs.  and  the  cut-off  is  lengthened  to 
58  per  cent  of  the  stroke,  the  steam-consumption  is  increased 


ECONOMY  OF  STEAM-ENGINES.  423 

to  30.2  Ibs.  per  horse-power  per  hour,  the  horse-power  being 
then  173.      The  gain  from  using  the  shorter  cut-off  is 

30.2  —  24.2 

-  X   ioo  =  20  per  cent. 

A  similar  comparison  for  the  same  engine  running  with  a 
vacuum  and  with  steam  in  the  jacket  shows  even  a  larger  dif- 
ference. Thus  in  test  1 6  the  steam-pressure  is  84  Ibs.  and 
the  cut-off  is  at  11.5  per  cent  of  the  stroke,  the  horse-power 
is  176,  and  the  steam-consumption  per  horse-power  per  hour 
is  16.9  Ibs.,  while  the  consumption  for  about  the  same  power 
in  test  44  is  25.4  Ibs.  of  steam  per  horse-power  per  hour,  the 
steam-pressure  being  35  and  the  cut-off  at  58  per'c  nt  of  the 
stroke ;  here  the  gain  from  using  the  shorter  cut-off  is 

25.4  —  16.9 

^  X   ioo  =  33  per  cent. 
25.4 

Considering  also  that  automatic  engines  are  usually  well 
built  and  carefully  attended  to,  while  throttling-engines  are 
often  cheaply  built  and  neglected,  the  good  reputation  of  the 
one  and  the  bad  reputation  of  the  other  are  easily  accounted 
for. 

It  is,  however,  far  from  certain  that  an  automatic  engine 
will  have  a  decided  advantage  over  a  throttle-engine,  provided 
the  latter  is  skilfully  designed,  well  built  and  cared  for,  and 
arranged  to  run  at  the  proper  cut-off.  Considering  the  rapid 
increase  in  steam-consumption  per  horse-power  per  hour  when 
the  cut-off  is  unduly  shortened,  it  is  not  unreasonable  to  ex- 
pect as  good  if  not  better  results  from  a  simple  throttling- 
engine  than  from  an  automatic  engine  when  both  are  run  for 
a  large  part  of  the  time  at  reduced  power. 

The  disadvantage  of  running  a  compound  or  a  triple  en- 
gine with  too  little  expansion  can  be  seen  by  comparing  the 
two  tests  on  the  engine  of  the  Rush  (Table  XXXII,  p.  388); 
on  the  other  hand  the  great  disadvantage  of  too  much  expan- 
sion is  made  evident  from  the  tests  on  the  engine  in  the  lab- 


424  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

oratory  of  the  Massachusetts  Institute  of  Technology  (Table 
XXXIII,  p.  392).  Considering  that  the  allowable  variation 
from  the  most  economical  cut-off  is  more  limited  for  a  com- 
pound or  a  triple  engine,  it  appears  that  there  is  less  reason 
for  using  an  automatic  governor  instead  of  a  throttling  gov- 
ernor for  compound  and  triple  engines  than  there  is  with  sim- 
ple engines.  Nevertheless  the  most  economical  engines  (sim- 
ple, compound,  or  triple)  are  automatic  engines. 

Effect  of  Speed  on  Condensation. — Though  the  con- 
densation of  steam  on  the  walls  of  the  cylinder  of  an  engine 
is  very  rapid,  it  is  not  instantaneous.  It  appears  reasonable 
that  the  amount  of  condensation,  and  consequently  the  in- 
fluence of  the  cylinder-walls,  may  be  reduced  by  increasing 
the  speed  of  revolution.  This  conclusion  is  confirmed  by  the 
results  of  the  investigations  by  Callendar  and  Nicolson, 
and  also  by  the  tests  on  the  Willans  engine.  Table  IX, 
page  349,  shows  that  the  condensation  per  stroke  was  re- 
duced from  0.0159  to  0.0074  by  increasing  the  revolutions 
from  46  to  97  per  minute.  It  must  be  borne  in  mind  in 
this  connection  that  the  effect  of  external  radiation  and  con- 
vection is  nearly  proportional  to  the  time,  and  that,  conse- 
quently, its  influence  is  more  pronounced  at  low  speeds  than 
at  high  speeds.  Since  the  engine  used  by  Callendar  and 
Nicolson  was  run  at  relatively  low  speeds  and  small  powers, 
the  influence  of  external  radiation  and  conduction  must  have 
been  abnormally  large,  and  consequently  an  increase  of  speed 
had  notable  effect  in  the  manner  just  explained. 

Table  XXXVIII,  page  403,  gives  four  sets  of  three  tests 
each  on  the  simple  non-condensing  Willans  engine ;  the  three 
tests  of  a  set  were  intended  to  be  made  at  100,  200,  and  400 
revolutions,  all  other  conditions  for  the  set  being  the  same. 
Each  set  shows  a  notable  gain  in  economy  and  a  notable 
reduction  in  condensation  on  account  of  the  increase  of  speed. 
Thus  a  comparison  of  tests  8  and  10  shows  that  the  con- 
densation is  reduced  by  nearly  one  half,  and  that  there  is  a 
gain  of  more  than  20  per  cent  in  steam-consumption,  by  in- 


ECONOMY  OF  STEAM-ENGINES.  425 

creasing  the  speed  from  1 1 1  to  408  revolutions  per  minute. 
The  other  sets  of  tests  show  similar  results,  as  do  also  three 
sets  of  speed  tests  at  the  bottom  of  Table  XL  on  the  com- 
pound non-condensing  engine. 

In  the  development  of  applications  of  electricity  there  has 
been  a  tendency  to  use  high-speed  engines,  which  can  either 
be  connected  directly  to  the  electric  generators,  or  connected 
to  them  by  belting  without  an  intermediate  shaft.  In  general 
the  engines  used  have  consumed  more  steam  per  horse-power 
per  hour  than  slow-speed  engines  running  under  similar  con- 
ditions. This  result  may  be  attributed  to  the  type  of  engine, 
which  is  virtually  a  plain  slide-valve  engine  controlled  by  a 
shaft-governor.  In  order  that  the  valve  may  be  controlled 
directly  by  the  governor  it  must  move  freely,  and  con- 
sequently some  form  of  balanced  valve  or  piston-valve  must 
be  used.  Such  valves  may  be  tight  when  properly  adjusted 
and  in  good  condition,  but  they  are  likely  to  leak  in  ordinary 
service.  And  again,  in  order  that  the  engine  may  run  with  a 
comparatively  early  cut-off,  the  engine  must  have  a  large 
clearance  or  else  the  compression  will  be  excessive.  Com- 
pound high-speed  engines  have  been  developed  to  meet  the 
requirements  of  this  service,  and  have  given  satisfaction  when 
run  at  full  power.  At  reduced  power  certain  difficulties  arise, 
as  stated  on  page  420,  especially  when  the  cut-off  for  the 
low-pressure  cylinder  is  fixed. 

Steam-turbines. — Many  attempts  have  been  made  from 
time  to  time  to  devise  some  form  of  impulse  or  reaction  wheel 
that  can  be  driven  by  the  direct  action  of  steam.  The  funda- 
mental difficulty  in  devising  such  a  wheel  is  the  high  velocity 
of  steam  when  flowing  out  of  an  orifice,  for  the  linear  velocity 
of  the  wheel  must  have  a  proper  relation  to  the  velocity  of 
the  steam  in  order  to  obtain  economical  results. 

Fig.  83  represents  the  essential  parts  of  a  Laval  steam- 
turbine,  consisting  of  a  wheel  which  carries  a  large  number  of 
curved  steel  cups  or  buckets  to  receive  the  jet  of  steam  from 
a  nozzle  set  at  an  angle.  The  figure  shows  only  one  nozzle, 


426 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


but  a  number  may  be  used,  the  wheel  in  question  having  four. 
Three  of  the  nozzles  have  a  diameter  of  0.138  of  an  inch  at 
the  throat  and  one  a  diameter  of  0.157  of  an  inch.  All  the 
nozzles  are  diverging  toward  the  exit  end  and  are  intended  to 
give  an  adiabatic  expansion  of  the  steam  to  the  pressure  of 
the  atmosphere,  so  as  to  develop  the  maximum  kinetic  energy 


Turbine  Wheel 


at  the  exit.  The  wheel  runs  at  approximately  24,000  revolu- 
tions per  minute,  and  as  it  has  a  diameter  of  about  five  inches 
at  the  middle  of  the  buckets,  their  velocity  is  about  30,000 
feet  per  minute  or  500  feet  per  second.  The  velocity  of  steam 
flowing  from  a  pressure  of  125  pounds  by  the  gauge  or  140 
pounds  absolute,  with  continuous  expansion  to  the  pressure 
of  the  atmosphere,  is  about  2800  feet  per  second. 

The  results  of  tests  on  this  turbine  by  Professor  Goss  are 
given  in  Table  XLIII.  It  is  reported  that  a  test  of  a  64 
horse  power  Laval  turbine  by  Prof.  J.  E.  Cederblom  gave  a 
steam-consumption  of  19.7  pounds  per  brake  horse-power  per 
hour  when  supplied  with  steam  at  about  100  pounds  by 
the  gauge,  and  exhausting  into  a  vacuum  of  26  inches  of 
mercury. 


ECONOMY  OF  STEAM-ENGINES. 


427 


TABLE   XLIII. 

TESTS    ON    A    LAVAL   STEAM-TURBINE. 
By  Prof.  W.  F^M.  Goss,  Trans.  Am.  Soc.  Mech.  Engs.,  vol.  xvii,  p.  81. 


Steam-pressure 

3 

w 

by  gauge. 

M 

I 

[ 

1* 

cfi 

• 

V 

_rt  ^ 

c 

x 

c 

B 

"§  ii 

o 

£ 

'1 

a^"S 

3  3 

Jm 

jjj 

4* 

t*  c 

11 

V 

M 

rt 

£ 

|H 

05 

CQ 

58 

K 

M 

i      21180 

0.00 

130 

17.1 

•  . 

2      25210    1.63 

42.2 

128.6 

3      20190    2.36 

1 

48.5 

99.8 

Four  nozzles  in  action,  three  hav- 
ing a  diameter  of  0.138  of  an  inch 
and  one  0.157  of  an  inch. 

4 

5 
6 

7 

20980 
18990 
20520 
21080 

2.97 

3.46 
4.38 

5-io 

• 

55-6 
61  .9 
70.8 
76.9 

85.7 
79.6 

71-5 

64.4 

8 

25520 

7-52 

* 

99.6 

53-6 

9 

24300 

8.24 

' 

104.4 

5i-3 

10 

23880 

10.33 

1 

126.3 

47-8 

Three  nozzles  in  action,  two  0.138 
of  an  inch  and  one  0.157  of  an 
inch  in  diameter. 

ii 

12 
13 
14 

17960 
2O92O 
21050 
24660 

o.oo 
3-95 
4-77 
6.50 

• 

31-3 
83-6 

93-4 
111.7 

67.8 
60.0 

53-3 

Two  nozzles  in  use,  each  0.138  of 
an  inch  in  diameter. 

15 

16 
17 

25220 
20300 
18920 

0.00 

i-95 
3-43 

• 

42.2 
83-5 

121.  1 

83-4 
65.0 

18      23900    3.87 

I27.O 

59-3 

The  Parsons  steam-turbine  has  a  number  of  turbines 
arranged  in  series  through  which  the  steam  passes  in  succes- 
sion, thus  breaking  up  the  difference  of  pressure  between  the 
supply  and  the  exhaust  into  a  number  of  steps;  consequently 
the  velocity  of  the  steam  impinging  onto  any  set  of  vanes  is 
comparatively  low.  Instead  of  a  few  nozzles,  each  turbine 
has  a  series  of  guides  extending  entirely  around  the  wheel, 
thus  supplying  steam  to  all  the  vanes  of  the  movable  wheels 
at  the  same  time.  Table  XLIV  gives  the  results  of  tests  on 
a  Parsons  turbine  having  seven  separate  turbines  and  seven 
corresponding  steps  in  the  reduction  of  the  steam-pressure 
from  the  supply  to  the  exhaust;  the  low-pressure  turbine  was 


428 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


made  double,  thus  giving  eight  moving  wheels  in  all.  Later 
turbines  have  been  given  a  large  number  of  separate  turbines 
so  that  a  large  number  of  expansions  of  steam  is  attained,  and 
it  is  claimed  that  their  economy  is  as  good  as  that  of  the  best 
steam-engines. 

TABLE    XLIV. 

TESTS    ON    PARSON'S    STEAM-TURBINE. 

SIX  HIGH-PRESSURE  SINGLE  DISKS  J    ONE  LOW-PRESSURE  DOUBLE  DISK. 

By  Prof.  ALEX.  B.  W.  KENNEDY,  Engineering,  vol.  Ivi.  p.  126. 


72 

Q<3 

122 

/i6  n 

Steam-pressure,  pounds  per  square  inch  above 
atmosphere  

Q7 

Qd.    6 

QJ.    ^ 

Q7    I 

Corresponding  temperature  of  saturated  steam. 

336 

•3  C6 

334 

•371 

334 
4,01 

336 

•3QT 

Vacuum,  pounds  per  square  inch  

14..  "\ 

id..  ^ 

id  .0 

Id.    I 

Revolutions  per  minute  

46^^ 

Kilowatts  

27    Q 

44/D 

68  8 

no  8 

Electrical  horse-power  

»/*v 

07    c 

O2    2 

Td8    Z 

i^J 

Steam  per  kilowatt  per  hour   pounds.  .  . 

AA.    I 

y^-^ 

•2T      0 

27    O 

27    2 

Steam    per    electrical    horse-power   per    hour, 

•50     O 

JJ..^ 

0-3    a 

•/  »*J 

20  8 

2O    7 

J^'V 

CHAPTER    XVI. 
FRICTION   OF    ENGINES. 

THE  efficiency  and  economy  of  steam-engines  are  com- 
monly based  on  the  indicated  horse-power,  because  that 
power  is  a  definite  quantity  that  may  be  readily  determined. 
On  the  other  hand,  it  is  usually  difficult  and  sometimes  im- 
possible to  make  a  satisfactory  determination  of  the  power 
actually  delivered  by  the  engine.  A  common  way  of  deter- 
mining the  work  consumed  by  friction  in  the  engine  itself  is 
to  disconnect  the  driving-belt,  or  other  gear  for  transmitting 
power  from  the  engine,  and  to  place  a  friction-brake  on  the 
main  shaft;  the  power  developed  is  then  determined  by  aid 
of  indicators,  and  the  power  delivered  is  measured  by  the 
brake,  the  difference  being  the  power  consumed  by  friction. 
Such  a  determination  for  a  large  engine  involves  much 
trouble  and  expense,  and  may  be  unsatisfactory  since  the 
engine-friction  may  depend  largely  on  the  gear  for  transmit- 
ting power  from  the  engine,  especially  when  belts  or  ropes  are 
used  for  that  purpose. 

The  friction  of  a  pumping-engine  may  be  determined  from 
a  comparison  of  the  indicated  power  of  the  steam-cylinders 
with  the  indicated  work  of  the  pumps,  or,  better,  with  the 
work  done  in  lifting  water  from  the  well  and  delivering  it  to 
the  forcing-main.  But  the  friction  thus  determined  is  the 
friction  of  both  the  engine  and  the  pump.  Air-compressors 
and  refrigerating  machines  may  be  treated  in  the  same  way 
to  determine  the  friction  of  both  engine  and  compressor. 
Again,  the  combined  friction  of  an  engine  and  a  directly 
connected  electric  generator  may  be  determined  by  compar- 
ing the  indicated  power  of  the  engine  with  the  electric 

429 


430 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


output  of  the  generator,  allowing  for  electricity  consumed  or 
wasted  in  the  generator  itself. 

The  friction  of  a  steam-engine  may  consume  from  5  to  15 
per  cent  of  the  indicated  horse-power,  depending  on  the  type 
and  condition  of  the  engine.  The  power  required  to  drive 
the  air-pump  (when  connected  to  the  engine)  is  commonly 
charged  to  the  friction  of  the  engine.  It  is  usual  to  consider 
that  seven  per  cent  of  the  indicated  power  of  the  engine  is 
expended  on  the  air-pump.  Independent  air-pumps  which 
can  be  driven  at  the  best  speed  consume  much  less  power; 
those  of  some  United  States  naval  vessels  used  only  one  or 
two  per  cent  of  the  power  of  the  main  engines.  But  as  inde- 
pendent air-pumps  are  usually  direct-acting  steam-pumps, 
much  of  the  apparent  advantage  just  pointed  out  is  lost  on 
account  of  the  excessive  steam-consumption  of  such  pumps. 

Mechanical  Efficiency. — The  ratio  of  the  power  delivered 
by  an  engine  to  the  power  generated  in  the  cylinder  is  the 
mechanical  efficiency ;  or  it  may  be  taken  as  the  ratio  o.f  the 
brake  to  the  indicated  power.  The  mechanical  efficiency  of 
engines  varies  from  0.85  to  0.95,  corresponding  to  the  per 
cent  of  friction  given  above. 

The  following  table  gives  the  mechanical  efficiencies  of  a 
TABLE  XLV. 

MECHANICAL    EFFICIENCIES    OF    ENGINES. 


Kind  of  engine. 

Horse-  power. 

Efficiency. 

Simple  engines: 

2J. 

O   86 

««                ««          Hoadley  

8O 

O    QI 

High-speed    straight-line  

<;6 

o  96 

1  60 

o  81 

"       non-condensing  

100 

0.86 

Compound: 
Portable  

78 

o  88 

60 

0.88 

CQ 

O   QO 

288 

0.86 

I  IO 

O.  Q2 

64.3 

O.  Q1? 

576 

O.  QO 

FRICTION  OF  ENGINES.  431 

number  of  engines,  determined  by  brake  tests,  or,  in  case  of 
the  pumping-engines,  by  measuring  the  work  done  in  pump- 
ing waters. 

Initial  Friction  and  Load  Friction. — A  part  of  the  fric- 
tion of  an  engine,  such  as  the  friction  of  the  piston-rings  and 
at  the  stuffing-boxes  of  piston-rods  and  valve-rods,  may  be 
expected  to  remain  constant  for  all  powers.  The  friction  at 
the  cross-head  guides  and  crank-pins  is  due  mainly  to  the 
thrust  or  pull  of  the  steam-pressure,  and  will  be  nearly  pro- 
portional to  the  mean  effective  pressure.  Friction  at  other 
places,  such  as  the  main  bearings,  will  be  due  in  part  to  weight 
and  in  part  to  steam-pressure.  On  the  whole  it  appears 
probable  that  the  friction  may  be  divided  into  two  parts,  of 
which  one  is  independent  of  the  load  on  the  engine,  and  the 
other  is  proportional  to  the  load.  The  first  may  be  called  the 
initial  friction  and  the  second,  the  load  friction.  Progressive 
brake  tests  at  increasing  loads  confirm  this  conclusion. 

Table  XLVI  gives  the  results  of  tests  made  by  Walther- 
Meunier  and  Ludwig*  to  determine  the  friction  of  a  horizon- 
tal-receiver compound  engine,  with  cranks  at  right  angles  and 
with  a  fly-wheel,  grooved  for  rope-driving,  between  the 
cranks.  The  piston-rod  of  each  piston  extended  through  the 
cylinder-cover  and  was  carried  by  a  cross-head  on  guides,  and 
the  air-pump  was  worked  from  the  high-pressure  piston-rod. 
The  cylinders  each  had  four  plain  slide-valves,  two  for  admis- 
sion and  two  for  exhaust;  the  exhaust-valves  had  a  fixed 
motion,  but  the  admission-valves  were  moved  by  a  cam  so 
that  the  cut-off  was  determined  by  the  governor. 

The  main  dimensions  of  the  engine  were : 

Stroke    i.i       metres. 

Diameter  ;  small  piston 0.536  " 

large  piston 0.800  " 

piston-rods 0.080  " 

Diameter,  air-pump  pistons   0.360  " 

Stroke,  air-pump 0.476  " 

Diameter,  fly-wheel 6.610  " 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  vol.  Ivii,  p.  140. 


432  THERMODYNAMICS  OF   THE    STEAM-ENGINE. 

TABLE   XLVI. 

FRICTION    OF   COMPOUND    ENGINE. 

WALTHER-MEUNIER    and   LUDWIG,   Btdletin  de  la  Soc.  Ind.  de  Mulhouse, 

vol.  Ivii,  p.  140. 


Horse-powers  —  Chevaux  aux  vapeur. 

Condition. 

Friction. 

Efficiency. 

Indicated. 

Effective. 

Absorbed 
by  engine. 

I 

288.5 

249.0 

39-5 

0.137 

0.863 

2 

276.9 

238.9 

38.0 

0.138 

0.862 

3 
4 

5 

Compound 
condensing 

265.6 

243-7 
222.7 

228.9 

208.8 
188.7 

36.7 
34-9 
34-0 

0.139 
0.144 

0.153 

0.861 
0.856 
0.847 

6 

7 

air-pump. 

201.5 
180.4 

168.6 
148.5 

32-9 
3L9 

0.164 
0.178 

0.836 
o  822 

8 

158.1 

128.4 

29-7 

0.189 

0.811 

9 

136.1 

108.3 

27.8 

0.205 

0.795 

10 

I53-I 

128.4 

24.7 

0.161 

0.839 

1  1 

T2 
13 
14 
15 

16 

High- 
pressure 
cylinder 
only. 
Condensing 

142.0 
130.9 
120.  I 
lOg.O 

97-5 
86.3 

118.3 
1  08  3 
98.2 

88.2 
78.1 
68.1 

23-7 

22.6 
21.9 
20.8 
19.4 

I8.3 

0.167 
0.173 
0.182 
0.191 
0.199 

O.2I2 

0.833 
0.827 

0.818 
0.809 
0.801 

0.788 

17 
18 

air-pump. 

75-7 
65-5 

58.0 
48.0 

17-7 
17-5 

0.234 

0.267 

0.766 
0.733 

iQ 

55-2 

37-9 

'      17-3 

0.313 

0.687 

20 

145-9 

128.4 

17-5 

O.I  2O 

0.880 

21 
22 

23 
24 

25 

High- 
pressure 
cylinder 
only. 
Nr>n 

135-7 

125  2 
II4.4 
103.9 

93-o 

118.3 
108.3 
98.2 
88.2 
78.1 

17.4 
16.9 

16.2 

15.7 
14.9 

0.129 

0.135 

0.142 
0.152 
0.160 

0.871 
0.865 
0.858 
0.848 
0.840 

26 

27 
28 

condensing, 
no  air-pump. 

82.0 

71-7 
61.6 

68.1 
58.0 
48.0 

13  9 
13.7 
13.6 

0.170 
0.191 

O.22I 

0.830 
0.809 
0-779 

29 

51-3 

37-9 

13-4 

O.262 

0.738 

The  engine  during  the  experiments  made  58  revolutions 
per  minute.  The  air-pump  had  two  single-acting  vertical 
pistons. 

Each  experiment  lasted  10  or  20  minutes,  during  which 
the  load  on  the  brake  was  maintained  constant,  and  indicator- 
diagrams  were  taken.  The  experiments  with  small  load  on 


FRICTION  OF  ENGINES. 


433 


the  brake  (numbers  9,  18,  19,  28,  and  29)  were  difficult  and 
uncertain. 

The  first  nine  tests  were  made  with  the  engine  working 
compound.  Tests  10  to  19  were  made  with  the  high-pressure 
cylinder  only  in  action  and  with  condensation,  the  low-pres- 
sure connecting-rod  being  disconnected.  Tests  20  to  29  were 
made  with  the  high-pressure  cylinder  in  action,  without  con- 
densation. 

The  results  of  these  tests  are  plotted  on  Fig.  84,  using  the 


-40 


ABSCISSAE,    EFFECTIVE  HORSEPOWER. 
ORDINATE8,    FRICTION   HORSEPOWER. 


50 


100 


150 


200 


260 


FIG.  84. 

effective  horse-power  for  abscissae  and  the  brake  horse-powers 
for  ordinates.  Omitting  tests  with  small  powers  (for  which 
the  brake  ran  unsteadily),  it  appears  that  each  series  of  tests 
can  be  represented  by  a  straight  line  which  crosses  the  axis  of 
ordinates  above  the  origin ;  thus  affording  a  confirmation  of 
the  assumption  that  an  engine  has  a  constant  initial  friction, 
and  a  load  friction  which  is  proportional  to  the  load. 

Now  the  initial  friction  which  depends  on  the  size  and 
construction  of  the  engine  may  be  assumed   to  be  proper- 


434  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

tional  to  the  normal  net  or  brake  horse-power,  Pn  ,  which  the 
engine  is  designed  to  deliver,  and  may  be  represented  by 


where  a  is  a  constant  to  be  determined  from  a  diagram  like 
Fig.  84.  If  P  is  the  net  horse-power  delivered  by  the  engine 
at  any  time,  then  the  load  friction  corresponding  is 

*P, 

where  b  is  a  second  constant  to  be  determined  from  experi- 
ments. The  total  friction  of  the  engine  will  be 

F=aPn+bP,      .....      (308) 
so  that  the  indicated  power  of  the  engine  will  be 

I.H.P.  =P+aP,  +  bP  =  aPn  +  (i  +  b)P.       (309) 
The  mechanical  efficiency  corresponding  will  be 

I.H.P.  -  F  P 

I.H.P.        =  nOV     '      •      '     <3I°) 

The  compound  condensing  engine  for  which  tests  are 
represented  by  Fig.  84  developed  290  I.H.P.  and  delivered 
250  horse-power  to  the  brake,  so  that  40  horse-power  was 
consumed  in  friction.  The  diagram  shows  also  that  the  initial 
friction  was  20  horse-power,  and  consequently  the  load  fric- 
tion was  20  horse-power.  The  values  of  a  and  b  are  conse- 
quently 

a  =  20  -r-  250  =  0.07; 

b  =  (40  —  20)  -r-  250  =  0.07. 

The  indicated  horse-power  for  a  given  load  P  is 


I.H.P.  =  o.o7Pn+  i.oyP.      .     .      .     (311) 

Similar  equations  can  be  deduced  for  the  engine  with 
steam  supplied  to  the  small  cylinder  only;  but  as  the  engine 
is  not  then  in  normal  condition  they  are  not  very  useful. 

The  maximum  efficiency  of  this  engine  is 

250  -T-  290  =  0.86; 


FRICTION  OF  ENGINES. 


435 


but  at  half  load  (125  horse-power)  the  indicated  horse-power  is 
I.H.P.  =  0.07  X  250+  1.07  X  125  =  151, 

and  the  efficiency  is 

125  -r-  151  =  0.83. 

TABLE  XLVII. 

FRICTION    OF    CORLISS    ENGINE   AT    CREUSOT. 

By  F.   DELAFOND,  Annales  des  Mines,  1884. 
Condensing  with  air-pump,  tests  1-33. 
Non-condensing  without  air-pump,  tests  34-46. 


Cut-off  frac- 
tion of 
stroke. 

Pressure  at 
cut-off,  kilos 
per  sq.  cm. 

Revolutions 
per  minute. 

Horse-power—  Cheval  i  vapeur. 

Indicated. 

Effective. 

Absorbed 
by  engine. 

I 

0.039 

0.64 

64.0 

27.8 

16.3 

"•5 

2 

0.044 

2.40 

68.5 

60.0 

37-6 

22.4 

3 

0.044 

2.90 

65.0 

67.2 

45-2 

22.0 

4 

0.065 

4.90 

64.0 

117.0 

88.7 

28.3 

5 

0.065 

6.20 

6r.o 

138.5 

106.3 

32-2 

6 

0.065 

7.10 

64.0 

163.2 

I2Q.2 

34-0 

7 

0.065 

7.60 

64.0 

185.0 

144.6 

40.4 

8 

O.IOO 

0.16 

58.0 

21.0 

10.6 

10.4 

9 

0.106 

i-55 

60.0 

61.9 

42.3 

19.6 

10 

O.IOO 

2.82 

57-3 

82.7 

61.0 

21.7 

ii 

0.096 

4.80 

58-3 

135.3 

106.7 

28.6 

12 

0.128 

4.82 

58-3 

154.5 

124.8 

29.7 

13 

0.142 

0.76 

62.0 

42.3 

28.4 

I3«9 

14 

0.137 

0.71 

60.6 

44-3 

28.7 

15-6 

16 

0.132 
0.147 

2.50 
2.60 

54-o 
61.6 

79-5 

IOO.O 

59-8 
78.2 

I9.7 
21.8 

11 

0.155 
0.167 

4-65 

0.22 

60.0 
61.0 

177.2 
40.2 

145.0 
27-9 

32.2 
12.3 

19 

0.197 

2-55 

57-2 

no.  8 

83-3 

27-5 

20 

0.273 

0.40 

62.3 

50.2 

33-8 

16.4 

21 
22 

0.264 
0.240 

j$ 

63.3 
62.0 

89.t 
87.2 

61.8 
63.1 

27.3 
24.1 

23 

0.245 

56.0 

116.0 

29.0 

24 

0.260 

4.76 

58.0 

209.4 

178.0 

3L4 

25 

0-335 

0.25 

59-0 

47-2 

32-5 

14.7 

26 

0.339 

1.94 

58-3 

111.7 

90.0 

21.7 

2 

0-338 

i 

2.97 
0.47 

61.0 
59-3 

161.8 
81.3 

Il37:l 

28.8 
14.1 

29 

i 

o-47 

61.0 

80.8 

67.9 

12.9    . 

i 

i.  60 

61.6 

148.5 

128.4 

20.1 

31 

i 

2.70 

61.5 

216.5 

191.0 

25-5 

32 

i 

2.70 

61.5 

215-3 

191  .0 

24-5 

33 

0.50 

0.70 

61.5 

15.8 

0.0 

15.8 

34 

0.120 

6.00 

60.0 

132.5 

107.5 

25.0 

35 

0.106 

7.00 

53-o 

125.0 

103.0 

22.0 

36 

0.120 

7-50 

62.0 

172.0 

148.0 

24.0 

39 
40 

0.150 
0.262 
0.293 
0.371 

4-57 
4-50 
4  55 
4.40 

55  -° 

59-o 

60.0 

102.3 
149.2 
171.8 
J95-3 

86.5 
132-3 
153-8 
177.2 

16.9 

18.0 
18.1 

0.348 

2-75 

58.0 

85-1 

73«  * 

12.0 

42 

0.348 

58.5 

84-8 

7I.I 

13-7 

43 

0.440 

3-48 

62.0 

151.0 

134.3 

l6.7 

44 

O.  Ill 

3-30 

62.0 

12.8 

0.0 

12.3 

45 

0.50 

i.  20 

62.0 

12.3 

0.0 

12-3 

46 

I 

0.50 

62.0 

10.45 

o.o 

10.45 

THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Table  XLVII  gives  the  results  of  a  large  number  of  brake 
tests  made  on  a  Corliss  engine  at  Creusot  by  M.  F.  Delafond, 
both  with  and  without  a  vacuum,  and  with  varying  steam- 
pressures  and  cut-off.  The  tests  with  a  vacuum  are  plotted 
on  Fig.  85,  and  those  without  a  vacuum  are  given  in  Fig.  86. 
In  both  figures  the  abscissae  are  the  indicated  horse-powers,  and 
the  ordinates  are  the  friction  horse-powers.  Most  of  the  tests 
are  represented'  by  dots;  those  tests  which  were  made  with 
the  most  economical  cut-off  (one  sixth  for  the  engine  with 


• 

>< 

^ 

• 

+  ' 

^> 

** 

• 

• 

•             ^^ 

/ 

0 

+  \/ 

/ 

^r^ 

Absci 

ssae,  in 

dicatec 

[  horse] 

K>wer 

<s 

'<£ 

• 

( 

( 

Ordin 

ates,  fr 

iction  ] 

lorsepo 

wer 

^ 

3           20          40           60           80          100        120         140         160         180         20 

FIG.  85. 

condensation  and  one  third  without)  are  represented  by 
crosses.  A  few  tests  with  very  long  cut-off,  on  Fig.  84,  are 
represented  by  circles.  The  straight  lines  on  both  figures  are 
drawn  to  represent  the  tests  indicated  by  crosses.  In  general 
the  points  representing  tests  with  short  cut-off  and  high 
steam-pressure  lie  above  the  lines,  and  points  representing 
tests  with  long  cut-off  and  low  steam-pressure  lie  below  the 
lines,  though  there  are  some  notable  exceptions  to  this  rule. 
The  circles  on  Fig.  84,  representing  tests  with  cut-off  near  the 


FRICTION  OF  ENGINES. 


437 


end  of  the  stroke,  show  much  less  friction  than  the  other  tests. 
The  tests  on  this  engine  show  clearly  that  both  initial  and 
load  friction  are  affected  by  the  cut-off  and  the  steam-pres- 
sure, and  that  friction  tests  should  be  made  at  the  cut-off 
which  the  engine  is  expected  to  have  in  service. 


20 


)scissa< 
Ordinate 


fricti 


indicated  horse pow 


n  hors  ;power 


inn 
FIG.  86. 


120 


140         160         180        200 


The  initial  friction  was  eight  horse-power  both  with  and 
without  condensation.  But  Table  XXX  shows  that  the 
engine  with  condensation  gave  the  best  economy  when  it 
indicated  160  horse-power;  the  friction  was  then  30  horse- 
power, so  that  the  net  horse-power  was  130,  which  will  be 
taken  for  the  normal  horse-power  Pn.  Consequently 

a  =  8  -r-  130  =  0.06; 

b  —  (30  —  8)  -r-  130  =  0.17. 

.-.     I.H.P.  =  o.o62fn  +  1. 17/>       .     .     (312) 

In  like  manner  Table  XLVII  shows  the  best  economy 
without  condensation,  for  about  100  indicated  horse-power, 
for  which  the  friction  is  14  horse-power,  leaving  86  for  the 
normal  power  of  the  engine.  Consequently 

a  =  8  -T-  86  =  0.09; 

b  =  (14  —  8)  -r-  86  =  0.07. 

.-.     I.H.P.  =  0.09/^4-  i. Q7/>.   .     .     .     (313) 


438 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


The  increased  value  of  a  for  the  non-condensing  engine  is 
due  directly  to  the  reduction  in  the  economical  power  of  the 
engine;  on  the  other  hand,  the  reduction  in  the  value  of  b  is 
due  to  the  omission  of  the  air-pump. 

Thurston's  Experiments. — As  a  result  of  a  large  number 
of  tests  on  non-condensing  engines,  made  under  his  direction 
or  with  his  advice,  Prof.  R.  H.  Thurston  *  concludes  that, 
for  engines  of  that  type,  the  friction  is  independent  of  the 
load,  and  that  it  can,  in  practice,  be  determined  by  indicating 
the  engine  without  a  load. 

TABLE  XLVIII. 

FRICTION    OF    NON-CONDENSING    ENGINE. 

STRAIGHT-LINE    ENGINE,  8    INCHES    DIAMETER,   14   INCHES    STROKE. 


No.  of 
Diagram. 

Boiler- 
pressure, 

Revolutions. 

Brake  H.  P. 

I.  H.  P. 

Frictional  H.  P. 

I 

50 

332 

4.06 

7.41 

3-35 

2 

65 

229 

4.98 

7.58 

2.60 

3 

63 

230 

6.00 

10.00 

4.00 

4 

69 

230 

7.00 

10.27 

3-27 

5 

73 

230 

8.10 

"•75 

3-65 

6 

77 

230 

9.00 

12.70 

3-70 

7 

75 

230 

10.00 

14.02 

4.02 

8 

80 

230 

II.OO 

14.78 

3-78 

9 

80 

230 

12.00 

15-17 

3-17 

10 

85 

230 

13.00 

15.96 

2.96 

n 

75 

230 

14.00 

16.86 

2.86 

12 

70 

230 

15.00 

17.80 

2.80 

13 

72 

231 

20.10 

22.07 

i-97 

14 

75 

230 

25.00 

28.31 

3-31 

15 

60 

229 

29-55 

33-04 

3-40 

16 

58 

229 

34-86 

37-20 

2.34 

17 

70 

229 

39-85 

43-04 

3.19 

18 

85 

230 

45-00 

47-79 

2.78 

19 

90 

230 

50.00 

52.60 

2.60 

20 

85 

230 

55-oo 

57-54 

2.54 

Table  XLVIII  gives  the  details  of  one  series  of  tests. 
The  friction  horse-power  is  small  in  all  the  tests,  and  the 
variations  are  small  and  irregular,  and  appear  to  depend  on 
the  state  of  lubrication  and  other  minor  causes  rather  than  on 
the  change  of  load. 

*  Trans,  of  the  Am.  Soc.  of  Mech.  Engrs.,  vols.  viii,  ix,  and  x. 


FRICTION  OF  ENGINES.  439 

Distribution  of  Friction.  —  As  a  consequence  of  his  con- 
clusion in  the  preceding  section,  Professor  Thurston  says 
that  the  friction  of  an  engine  may  be  found  by  driving  it  from 
some  external  source  of  power,  with  the  engine  in  substan- 
tially the  same  condition  as  when  running  as  usual,  but  with- 
out steam  in  its  cylinder,  and  by  measuring  the  power 
required  to  drive  it  by  aid  of  a  transmission  dynamometer. 
Extending  the  principle,  the  distribution  of  friction  among  the 
several  members  of  the  engine  may  be  found  by  disconnecting 
the  several  members,  one  after  another,  and  measuring  the 
power  required  to  run  the  remaining  members. 

The  summary  of  a  number  of  tests  of  this  sort,  made  by 
Prof.  R.  C.  Carpenter  and  Mr.  G.  B.  Preston,  are  given  in 
Table  XLIX.  Preliminary  tests  under  normal  conditions 
showed  that  the  friction  of  the  several  engines  was  practically 
the  same  at  all  loads  and  speeds. 

The  most  remarkable  feature  in  this  table  is  the  friction  of 
the  main  bearings,  which  in  all  cases  is  large,  both  relatively 
and  absolutely.  The  coefficient  of  friction  for  the  main 
bearings,  calculated  by  the  formula 

33000  H.P. 


is  given  in  Table  L.  p  is  the  pressure  on  the  bearings  in 
pounds  for  the  engines  light,  and  plus  the  mean  pressure  on 
the  piston  for  the  engines  loaded;  c  is  the  circumference  of 
the  bearings  in  feet  ;  n  is  the  number  of  revolutions  per 
minute;  and  H.P.  is  the  horse-power  required  to  overcome 
the  friction  of  the  bearings. 

The  large  amount  of  work  absorbed  by  the  main  bearings 
and  the  large  coefficient  of  friction  appear  the  more  remark- 
able from  the  fact  that  the  coefficient  of  friction  for  car-axle 
journals  is  often  as  low  as  one-tenth  of  one  per  cent,  the 
difference  being  probably  due  to  the  difference  in  the  methods 
of  lubrication. 


440 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


TABLE  XLIX. 

DISTRIBUTION    OF    FRICTION. 


Parts  of  Engine. 

Percentages  of  Total  Friction. 

Straight-line  6x  12 
Balanced  Valve. 

Straight-line  6"  x  12" 
Unbalanced  Valve. 

7"  x  10"  Lansing  Iron 
Works—  Traction-  Lo- 
comotive Valve-gear. 

12"  x  18"  Lansing  Iron 
Works  —  Automatic 
Balanced  Valve. 

21"  x  20"  Lansing  Iron 
Works  —  Condensing 
Balanced  Valve. 

Main  Bearings             

47.0 

35-4 

35-0 

41  .6 

46.0 

Piston  and  Rod          .... 

32.9 

6.8 

5-4 

25.0 

5-i 
4.1 

21.  0 

13-0 

49.1 

21.8 

Crank  Pin  

Cross  Head  and  Wrist  Pin.   . 
Valve  and  Rod               .    . 

2-5 
5-3 

26.4 
4.0 

22.  0 

9-3 

21  .O 

Eccentric  Strap     .  .       

Q.O 

12.  O 

Total  

100.  0 

IOO.O 

IOO.O 

IOO.O 

IOO.O 

TABLE  L. 

COEFFICIENT    OF    FRICTION    FOR   THE    MAIN    BEARINGS    OF 
STEAM-ENGINES. 


c 

• 

"2 

§4l 

•=! 

1 

a 

s 

1 

c 

'C  be 

0  V 

o   . 

3  vi 

0    tt 

^  3 

^  ^ 

v?3 

iS 

o  *n 

o  i> 

*O 

o.£ 

Engine. 

3  C 

SI 

°CU 

°| 

If 

il 

1? 

£  e 

S.s 

'—  ^ 

tC  r  1 

3  ^ 

X 

&>••* 
'5 

g 

• 

o§ 

o    • 

11 

fc 

* 

5 

U-2 

U-2 

1) 
H 

6"  X  12"  Straight-line     

0.85 

1500 

.  IO 

.06 

*I2"  X  18"  Automatic  (L.  I.  W.)  .. 

3.70 

2600 

5 

.19 

•05 

190 

7"  X  10"  Traction  (L.  I.  W.)  — 

0.68 

500 

2f 

•  31 

.08 

200 

2i"  X  20"  Condensing  (L.  I.  W.) 

3-30 

4000 

rt 

.09 

.04 

206 

*The  12"  X  i&"  automatic  engine  was  new,  and  gave,  throughout,  an  ex- 
cessive amount  of  friction  as  compared  with  the  older  engines  of  the  same  class 
and  make. 


FRICTION  OF  ENGINES.  44l 

The  second  and  obvious  conclusion  from  Table  L  is  that 
the  valve  should  be  balanced,  and  that  nine  tenths  of  the 
friction  of  an  unbalanced  slide-valve  is  unnecessary  waste. 

The  friction  of  the  piston  and  piston-rod  is  always  con- 
siderable, but  it  varies  much  with  the  type  of  the  engine, 
and  with  differences  in  handling.  It  is  quite  possible  to 
change  the  effective  power  of  an  engine  by  screwing  up  the 
piston-rod  stuffing-box  too  tightly.  The  packing  of  both 
piston  and  rod  should  be  no  tighter  than  is  necessary  to  pre- 
vent perceptible  leakage,  and  is  more  likely  to  be  too  tight 
than  too  loose. 


CHAPTER    XVII. 
COMPRESSED   AIR. 

COMPRESSED  air  is  used  for  transmitting  power,  for  stor- 
ing energy,  and  for  producing  refrigeration.  Air  at  moderate 
pressure,  produced  by  blowing-engines,  is  used  in  the  produc- 
tion of  iron  and  steel;  and  currents  of  air  at  slightly  higher 
pressure  than  that  of  the  atmosphere  (produced  by  centrifugal 
fan-blowers)  are  used  to  ventilate  mines,  buildings,  and 
ships,  and  for  producing  forced  draught  for  steam-boilers. 
Attention  will  be  given  mainly  to  the  transmission  and  storage 
of  energy.  The  production  and  use  of  ventilating  currents 
require  and  are  susceptible  of  but  little  theoretical  treatment. 
Refrigeration  will  be  reserved  for  another  chapter. 

A  treatment  of  the  transmission  of  power  by  compressed 
air  involves  the  discussion  of  air-compressors,  of  the  flow  of 
air  through  pipes,  and  of  compressed-air  engines  or  motors. 
The  storage  of  energy  differs  from  the  transmission  of  power 
in  that  the  compressed  air,  which  is  forced  into  a  reservoir  at 
high  pressure,  is  used  at  a  much  lower  pressure  at  the  air- 
motor. 

Air-compressors. — There  are  three  types  of  machines 
used  for  compressing  or  moving  air:  (i)  piston  air-compressors, 
(2)  rotary  blowers,  (3)  centrifugal  blowers  or  fans. 

The  piston  air-compressor  is  always  used  for  producing 
high  pressures.  It  consists  of  a  piston  moving  in  a  cylinder 
with  inlet-  and  exit-valves  at  each  end.  Commonly  the  valves 
are  actuated  by  the  air  itself,  but  some  compressors  have  their 
valves  moved  mechanically.  Blowing-engines  are  usually 

442 


COMPRESSED   AIR.  443 

piston-compressors,  though  the  pressures  produced  are  only 
ten  or  twenty  pounds  per  square  inch. 

Rotary  blowers  have  one  or  more  rotating  parts,  so- 
arranged  that  as  they  rotate,  chambers  of  varying  capacity 
are  formed  which  receive  air  at  atmospheric  pressure,  com- 
press it,  and  deliver  it  against  a  higher  pressure.  They  are 
simple  and  compact,  but  are  wasteful  of  power  on  account  of 
friction  and  leakage,  and  are  used  only  for  moderate  pressures. 

Fan-blowers  consist  of  a  number  of  radial  plates  or  vanes 
fixed  to  a  horizontal  axis  and  enclosed  in  a  case.  When  the 
axis  and  the  vanes  attached  to  it  are  rotated  at  a  high  speed 
air  is  drawn  in  through  openings  near  the  axis  and  is  driven 
by  centrifugal  force  into  the  case,  from  which  it  flows  into  the 
delivery-main  or  duct.  Only  low  pressures,  suitable  for 
ventilation  and  forced  draught,  can  be  produced  in  this  way. 
But  little  has  been  done  in  the  development  of  the  theory  or 
the  determination  of  the  practical  efficiency  of  fan-blowers. 
Some  ventilating-fans  have  their  axes  parallel  to  the  direction 
of  the  air-current,  and  the  vanes  have  a  more  or  less  helicoidal 
form,  so  that  they  may  force  the  air  by  direct  pressure;  they 
are  in  effect  the  converse  of  a  windmill,  producing  instead  of 
being  driven  by  the  current  of  air.  They  are  useful  rather 
for  moving  air  than  for  producing  a  pressure. 

Fluid  Piston-compressors. — It  will  be  shown  that  the 
effect  of  clearance  is  to  diminish  the  capacity  of  the  com- 
pressor; consequently  the  clearance  should  be  made  as  small  as 
possible.  With  this  in  view  the  valves  of  compressors  and 
blowers  are  commonly  set  in  the  cylinder-heads.  Single- 
acting  compressors  with  vertical  cylinders  have  been  made  with 
a  layer  of  water  or  some  other  fluid  on  top  of  the  piston,  which 
entirely  fills  the  clearance-space  when  the  piston  is  at  the  end 
of  the  stroke.  An  extension  of  this  principle  gives  what  are 
known  as  fluid  piston-compressors.  Such  a  compressor  com- 
monly has  a  double-acting  piston  in  a  horizontal  cylinder 
much  longer  than  the  stroke  of  the  piston,  thus  giving  a  large 
clearance  at  each  end.  The  clearance-spaces  extend  upward 


444  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

to  a  considerable  height,  and  the  admission-  and  exhaust- 
valves  are  placed  at  or  near  the  top,  and  the  entire  clearance- 
space  is  filled  with  water.  The  spaces  and  heights  must  be 
so  arranged  that  when  the  piston  is  at  one  end  of  its  stroke 
the  water  at  that  end  shall  fill  the  clearance  and  cover  the 
valves,  and  at  the  other  end  the  water  shall  not  fall  to  the 
level  of  the  top  of  the  cylinder.  There  are  consequently  two 
vertical  fluid  pistons  actuated  by  a  double-acting  horizontal 
piston.  It  is  essential  that  the  spaces  in  which  the  fluid 
pistons  act  shall  give  no  places  in  which  air  may  be  caught  as 
in  a  pocket,  and  that  there  are  no  projecting  ribs  or  other 
irregularities  to  break  the  surface  of  the  water;  and,  further, 
the  compressor  must  be  run  at  a  moderate  speed.  The  water 
forming  the  fluid  pistons  becomes  heated  and  saturated  with 
air  by  continuous  use,  and  should  be  renewed. 

Air-pumps  used  with  condensing-engines  or  for  other 
purposes  may  be  made  with  fluid  pistons  which  are  renewed 
by  the  water  coming  with  the  air  or  vapor.  In  case  the  water 
thus  supplied  is  insufficient,  water  from  without  may  be 
admitted,  or  water  from  the  delivery  may  be  allowed  to  flow 
back  to  the  admission  side  of  the  pump. 

Displacement-compressors. — When  a  supply  of  water 
under  sufficient  head  is  available,  air  may  be  compressed  in 
suitably  arranged  cylinders  or  compressors  by  direct  action  of 
the  water  on  air,  compressing  it  and  expelling  it  by  displace- 
ment. Such  compressors  are  very  wasteful  of  power,  and  in 
general  it  is  better  to  use  water-power  for  driving  piston- 
compressors,  properly  geared  to  turbine-wheels  or  other 
motors. 

Cooling  during  Compression. — There  is  always  a  con- 
siderable rise  of  temperature  due  to  compressing  air  in  a 
piston  air-compressor,  which  is  liable  to  give  trouble  by  heat- 
ing the  cylinder  and  interfering  with  lubrication.  Blowing- 
engines  which  produce  only  moderate  pressures  usually  have 
their  cylinders  lubricated  with  graphite,  and  no  attempt  is 
made  to  -cool  them.  All  compressors  which  produce  high 


COMPRESSED   AIR.  445 

pressures  have  their  cylinders  cooled  either  by  a  water-jacket 
or  by  injecting  water,  or  by  both  methods. 

Since  the  air  after  compression  is  cooled  either  purposely 
or  unavoidably,  there  would  be  a  great  advantage  in  cooling 
the  air  during  compression,  and  thereby  reducing  the  work  of 
compression.  Attempts  have  been  made  to  cool  the  air  by 
spraying  water  into  the  cylinder,  but  experience  has  shown 
that  the  work  of  compression  is  not  much  affected  by  so 
doing.  The  only  effective  way  of  reducing  the  work  of  com- 
pression is  to  use  a  compound  compressor,  and  to  cool  the  air 
on  the  way  from  the  first  to  the  second  cylinder.  Three- 
stage  compressors  are  used  for  very  high  pressures.  It  is, 
however,  found  that  air  which  has  been  compressed  to  a  high 
pressure  and  great  density  is  more  readily  cooled  during  com- 
pression. 

Moisture  in  the  Cylinder. — If  water  is  not  injected  into 
the  cylinder  of  an  air-compressor  the  moisture  in  the  air  will 
depend  on  the  hygroscopic  condition  of  the  atmosphere. 
But  even  if  the  air  were  saturated  with  moisture  the  absolute 
and  the  relative  weight  of  water  in  the  cylinder  would  be 
insignificant.  Thus  at  60°  F.  the  pressure  of  saturated  steam 
is  about  one-fourth  of  a  pound  per  square  inch,  and  the  weight 
of  one  cubic  foot  is  about  0.0008  of  a  pound,  while  the  weight 
of  one  cubic  foot  of  air  is  about  0.08  of  a  pound.  If  the 
atmosphere  is  not  saturated,  then  the  watery  vapor  drawn  into 
the  compressor  with  the  air  will  follow  the  laws  of  superheated 
steam.  Now  the  adiabatic  equations  for  air  and  for  super- 
heated steam  are 

^1.405  _  ppw     and    prf  —  pp\  t 

so  that  the  only  effect  of  moisture  in  the  air  will  be  to  slightly 
reduce  the  exponent  of  the  adiabatic  equation.  This  conclu- 
sion probably  holds  when  the  cylinder  is  cooled  by  a  water- 
jacket. 

When  water  is  sprayed  into  the  cylinder  of  a  compressor 
the  temperature  of  the  air  and  the  amount  of  vapor  mixed 


446  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

with  it  vary,  and  there  is  no  ready  way  of  determining  its 
condition.  But,  as  has  been  stated,  the  spraying  of  water 
into  the  cylinder  does  not  much  reduce  the  work  of  compres- 
sion, and  consequently  it  is  probable  we  can  assume  that  the 
compression  always  follows  the  law  expressed  by  an  exponen- 
tial equation  ;  such  as 


The  value  to  be  given  to  n  is  not  well  known;  it  may  be 
as  small  as  1.2  for  a  fluid  piston-compressor,  and  it  may 
approach  1.4  when  the  cooling  of  the  air  is  ineffective,  as  is 
usually  the  case. 

Power   Expended.  —  The    indicator-diagram    of    an    air- 
compressor  with  no  clearance-space  is  represented  by  Fig.  87. 
Air    is   drawn   in    at   atmospheric   pressure 
in  the  part  of  the  cycle  of  operations  repre- 
.       sented  by  dc\  in  the  part  represented  by  cb 
the  air  is  compressed,  and  in  the  part  repre- 


FIG.  87.  sented    by   ba   it    is    expelled    against    the 

higher  pressure. 

If/,  is  the  specific  pressure  and  vl  the  specific  volume  of 
one  pound  of  air  at  atmospheric  pressure,  and  /,  and  z/9 
corresponding  quantities  at  the  higher  pressure,  then  the  work 
done  by  the  atmosphere  on  the  piston  of  the  compressor 
while  air  is  drawn  in  is  /,^.  Assuming  that  the  compression 
curve  cb  may  be  represented  by  an  exponential  curve  having 

the  form 

pvn  =  pp?  =  const., 

then  the  work  of  compression  is 


The  work  of  expulsion  from  b  to  a  is 


n 


COMPRESSED    AIR.  447 

The  effective  work  of  the  cycle  is  therefore 


Equation  (314)  gives  the  work  done  to  compress  one 
pound  of  air,  p^  and  /2  being  specific  pressures  (in  pounds  per 
square  foot),  and  vl  the  specific  volume,  which  may  be 
calculated  by  aid  of  the  equation 

pv      p0v. 


T         T.' 

in  which  the  subscripts  refer  to  the  normal  properties  of  air 
at  freezing-point  and  at  atmospheric  pressure. 

If,  instead  of  the  specific  volume  vlt  we  use  the  volume 
Vl  of  air  drawn  into  the  comi  ressor  we  may  readily  transform 
equation  (314)  to  give  the  horse-power  directly,  obtaining 


H-r-  =  7^T    -7S       T         -'     .    •     -     (315) 


where  /,  is  the  pressure  of  the  atmosphere  in  pounds  per 
square  inch,  and  n  is  the  exponent  of  the  equation  represent- 
ing the  compression  curve,  which  may  vary  from  1.4  for  dry- 
air  compressors  to  1.2  for  fluid  piston-compressors. 

Effect  of  Clearance. — The  indicator-diagram  of  an  air- 
compressor  with  clearance  may  be  represented  by  Fig.   88. 
The  end  of  the  stroke  expelling  air  is  at  #, 
and  the  air  remaining  in  the   cylinder  ex- 
pands from  a  to  d,  till  the  pressure  becomes 
equal   to  the   pressure  of  the    atmosphere 
before  the  next  supply  of  air  is  drawn  in. 
The  expansion  curve  ad  may  commonly  be 
represented  by   an    exponential    equation    having  the  same 
exponent  as  the  compression  curve  cb,  in  which  case  the  air 


448  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

in  the  clearance  acts  as  a  cushion  which  stores  and  restores 
energy,  but  does  not  affect  the  work  done  on  the  air  passing 
through  the  cylinder.  The  work  of  compressing  one  unit  of 
weight  of  air  in  such  a  compressor  may  be  calculated  by  aid 
of  equation  (312),  but  the  equation  (315)  for  the  horse-power 
cannot  be  used  directly. 

The  principal  effect  of  clearance  is  to  increase  the  size  of 
the  cylinder  required  for  a  certain  duty  in  the  ratio  of  the 
entire  length  of  the  diagram  in  Fig.  88  to  the  length  of  the 
line  dc. 

Let  the  clearance  be  -  -  part  of  the  piston  displacement. 

At  the  beginning  of  the  rilling  stroke,  represented  by  the 
point  a,  the  volume  will  be  filled  with  air  at  the  pressure/,. 
After  the  expansion  represented  by  ad  the  air  in  the  clearance 
will  have  the  pressure  p^  and,  assuming  that  the  expansion 
follows  the  law  expressed  by  the  exponential  equation 


its  volume  will  be 

Ll£& 


part  of  the  piston  displacement.     The  ratio  of  the  line  dc  to 
the  length  of  the  diagram  will  consequently  be 


ac  m  m 


and  this  is  the  factor  by  which  the  piston  displacement  cal- 
culated without  clearance  must  be  divided  to  find  the  actual 
piston  displacement. 

Temperature  at  the  End  of  Compression.  —  When  the 
air  in  the  compressor-cylinder  is  dry  or  contains  only  the 
moisture  brought  in  with  it,  it  may  be  assumed  that  the 
mixture  of  air  and  vapor  follows  the  law  of  perfect  gases, 


COMPRESSED   AIR.  449 

which,  combined  with  the  exponential  equation 
gives 


from  which  the  final  temperature  71,  at  the  end  of  compression 
may  be  determined  when  Zi  is  known.  When  water  is  used 
freely  in  the  cylinder  of  a  compressor  the  final  temperature 
cannot  be  determined  by  calculation,  but  must  be  determined 
from  tests  on  compressors. 

Contraction  after  Compression.  —  Ordinarily  compressed 
air  loses  both  pressure  and  temperature  on  the  way  from  the 
compressor  to  the  place  where  it  is  to  be  used.  The  loss  of 
pressure  will  be  discussed  under  the  head  of  the  flow  of  air  in 
long  pipes;  it  should  not  be  large,  unless  the  air  is  carried 
a  long  distance.  The  loss  of  temperature  causes  a  contraction 
of  volume  in  two  ways:  first,  the  volume  of  the  air  at  a  given 
pressure  is  inversely  as  the  absolute  temperature;  second,  the 
moisture  in  the  air  (whether  brought  in  by  the  air  or  supplied 
in  the  condenser)  in  excess  of  that  which  will  saturate  the  air 
at  the  lowest  temperature  in  the  conduit,  is  condensed. 
Provision  must  be  made  for  draining  off  the  condensed  water. 
The  method  of  estimating  the  contraction  of  volume  due  to 
the  condensation  of  moisture  will  be  exhibited  later  in  the 
calculation  of  a  special  problem. 

Interchange  of  Heat.  —  The  interchanges  of  heat  between 
the  air  in  the  cylinder  of  an  air-compressor  and  the  walls  of 
the  cylinder  are  the  converse  of  those  taking  place  between 
the  steam  and  the  walls  of  the  cylinder  of  a  steam-engine,  and 
are  much  less  in  amount.  The  walls  of  the  cylinder  are  never 
so  cool  as  the  incoming  air  nor  so  warm  as  the  air  expelled  ; 
consequently  the  air  receives  heat  during  admission  and  the 
beginning  of  compression,  and  yields  heat  during  the  latter 
part  of  compression  and  during  expulsion.  The  presence  of 
moisture  in  the  air  increases  this  effect. 


450  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

Volume  of  the  Compressor-cylinder.  —  Let  a  compressor 
making  *n  revolutions  per  minute  be  required  to  deliver  F, 
cubic  feet  of  air  at  the  temperature  /,°  F.,  or  T°  absolute, 
and  at  the  absolute  pressure/,  pounds  per  square  inch,  at  the 
place  where  the  air  is  to  be  used.  Assuming  that  the  air  is 
dry  when  it  is  delivered  and  that  the  atmosphere  is  dry  when 
it  is  taken  into  the  compressor,  then  the  volume  drawn  into 
the  compressor  per  minute  at  the  temperature  Tl  and  the 
pressure/,  will  be 

'*••="     ......  (3i8) 


cubic  feet;  and  this  expression  will  be  correct  whatever  may 
be  the  intermediate  temperatures,  pressures,  or  condition  of 
saturation  of  the  air. 

If  the  compressor  has  no  clearance  the  piston  displacement 
will  be 


if  the  clearance  is  —  part  of  the  piston  displacement,  dividing 
by  the  factor  (316)  gives  for  the  piston  displacement 


expressed  in  cubic  feet. 

The  pressure  in  the  compressor-cylinder  when  air  is  drawn 
in  is  always  less  than  the  pressure  of  the  atmosphere,  and 
when  the  air  is  expelled  it  is  greater  than  the  pressure  against 
which  it  is  delivered.  From  these  causes  and  from  other 
imperfections  the  compressor  will  not  deliver  the  quantity  of 
air  calculated  from  its  dimensions,  and  consequently  the 
volume  of  the  cylinder  as  calculated,  whether  with  or  without 
clearance,  must  be  increased  by  an  amount  to  be  determined 
by  experiment. 


COMPRESSED    AIR.  451 

Compound  Compressors.  —  When  air  is  to  be  compressed 
from  the  pressure/,  to  the  pressure/,,  but  is  to  be  delivered 
at  the  initial  temperature  tlt  the  work  of  compression  may  be 
reduced  by  dividing  it  between  two  cylinders,  one  of  which 
takes  the  air  at  atmospheric  pressure  and  delivers  it  at  an 
intermediate  pressure/7  to  a  reservoir,  from  which  the  other 
cylinder  takes  it  and  delivers  it  at  the  required  pressure/.,, 
provided  that  the  air  be  cooled,  at  the  pressure/',  between 
the  two  cylinders. 

The  proper  method  of  dividing  the  pressures  and  of  pro- 
portioning the  volumes  of  the  cylinders  so  that  the  work  of 
compression  may  be  reduced  to  a  minimum  may  be  deduced 
from  equation  (314)  when  there  is  no  clearance  or  when  the 
clearance  is  neglected. 

The  work  of.  compressing  one  pound  of  air  from  the  pres 
sure  /,  to  the  pressure  /'  is 


The  work  of  compressing  one  pound  from  the  pressure  /' 

to  /,  is 


because  the  air  after  compression  in  the  first  cylinder  is  cooled 
to  the  temperature  /,  before  it  is  supplied  to  the  second 
cylinder,  and  consequently  p'v'  =  pj>^  The  total  work  of 
compression  is 


-  ,    .    (323) 


and  this  becomes  a  minimum  when 


452  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

becomes  a  minimum.      Differentiating  with  regard  to/',  and 
equating  the  first  differential  coefficient  to  zero,  gives 

/  =  V£A.  .     .     ,     .     v   .     .     (324) 

Since  the  air  is  supplied  to  each  cylinder  at  the  tempera- 
ture tlt  their  volumes  should  be  inversely  as  the  absolute 
pressures/!  and/'.  This  method  also  leads  to  an  equal  dis- 
tribution of  work  between  the  two  cylinders,  for  if  the  value 
of/'  from  equation  (324)  is  introduced  into  equations  (322) 
and  (323)  we  shall  obtain 


.  .  (325) 

and  the  total  work  of  compression  is 

-*  .....  (326) 


Three-stage  Compressors.  —  When  very  high  pressures 
are  required,  as  where  air  is  used  for  storing  energy,  it  is  cus- 
tomary to  use  a  compressor  with  a  series  of  three  cylinders, 
through  which  the  air  is  passed  in  succession,  and  to  cool  the 
air  on  the  way  from  one  cylinder  to  the  next.  If  the  initial 
and  final  pressures  are  p^  and  /„  and  if  /'  and  p"  are  the 
pressures  in  the  intermediate  receivers  in  which  the  air  is 
cooled,  the  conditions  for  most  economical  compression  may 
be  deduced  in  the  following  way: 

The  work  of  compressing  one  pound  of  air  in  the  several 
cylinders  will  be 


XV'-i.  (329) 


;  COMPRESSED   AIR.  453 

But  since  the  air  is  cooled  to  the  initial  temperature  on 
its  way  from  one  cylinder  to  the  other  so  that 


(330) 


consequently  the  total  work  of  compressing  one  pound  of  air 
will  be 


This  expression  will  be  a  minimum  when 


becomes  a  minimum  ;  that  is,  when 

_  *  »  —  i 

idW\          «-i/""       n-\p'~ 

(Wl'  =  —i±  —  5~  *a=»  »*  '•   (332) 

A  '  / 

and 

i  n  —  i 

«-!'-»        „  -  I         ~ 


P>  -  /'  - 

Equations  (328)  and  (329)  lead  to 

/'=/,/',   .......     (334) 

/"=//,:    .....    '.    .    (335) 

from  which  by  elimination  we  have 

S  =  Vf&«         ..;»•'»..      (336) 


454  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

and 


(337) 


Since  the  temperature  is  the  same  at  the  admission  to  each 
of  the  three  cylinders,  the  volumes  of  the  cylinders  should 
be  inversely  proportional  to  the  absolute  pressures/!,  /',  and 
p"  .  As  with  the  compound  compressors,  this  method  of 
arranging  a  three-stage  compressor  leads  to  an  equal  distribu- 
tion of  work  between  the  cylinders.  For,  if  the  values  of  /' 
and/"  from  equations  (336)  and  (337)  are  introduced  into 
equations  (327)  to  (329),  taking  account  also  of  the  equation 
(330)  we  shall  have 


wt=w,=  w.  =  Av=n     A      ~  r    ;  '   (338) 

and  consequently  the  total  work  of  compression  is 

.....    (339) 


Friction  and  Imperfections.  —  The  discussion  has  thus 
far  taken  no  account  of  friction  of  the  compressor  nor  of 
imperfections  due  to  delay  in  the  action  of  the  valves  and  to 
heating  the  air  as  it  enters  the  cylinder  of  the  compressor. 

From  comparisons  of  indicator-diagrams  taken  from  the 
steam-  and  the  air-cylinders  of  certain  combined  steam-engines 
and  air-compressors  at  Paris,  Professor  Kennedy  found  a 
mechanical  efficiency  of  0.845.  Professor  Gutermuth  found 
an  efficiency  of  0.87  for  a  new  Riedler  compressor.  It  will 
be  fair  to  assume  an  efficiency  of  0.85  for  compressors  which 
are  driven  by  steam-engines;  compressors  driven  by  turbines 
will  probably  be  affected  to  a  like  extent  by  friction. 

The  following  table  given  by  Professor  Unwin  *  shows  the 
effect  of  imperfect  valve-action  and  of  heating  the  entering 

*  Development  and  Transmission  of  Power,  p.  182. 


COMPRESSED   AIR. 


455 


air  as  deduced  from  tests  on  a  Dubois-Frangois  compressor 
which  had  a  diameter  of  18  inches  and  a  stroke  of  48  inches: 

RATIO   OF   ACTUAL   AND    APPARENT   CAPACITIES   OF   AN 
AIR-COMPRESSOR. 


Ratio  of  air 

delivered  at 

Piston  speed, 
feet  per 
minute. 

Revolutions 
per  minute. 

aimospheric 
pressure  and 
temperature  to 
volume  dis- 

placed by 

piston. 

80 

10 

0.94 

1  60 

20 

O.Q2 

200 

25 

0.90 

240 

30 

0.86 

280 

35 

0.78 

This  table  does  not  take  account  of  the  effect  of  clearance, 
nor  is  the  clearance  for  the  compressor  stated.  It  is  probable 
that  five  or  ten  per  cent  will  be  enough  to  allow  for  imperfect 
valve-action  after  the  effect  of  clearance  is  properly  calculated. 
The  effect  of  clearance  is  to  require  a  larger  volume  of  cylinder 
than  would  be  needed  without  clearance.  The  effect  of 
imperfect  valve-action  and  of  heating  of  the  entering  air  is  to 
require  an  additional  increase  in  the  size  of  the  cylinder  of  the 
air-compressor  and  also  to  increase  the  work  of  compression. 

Efficiency  of  Compression.— If  air  could 
be  so  cooled  during  compression  that  the 
temperature  should  not  rise  the  compres- 
sion line  cd,  Fig.  89,  would  be  an  isothermal 
line  and  the  work  of  compressing  one  pound 
of  air  would  be 


FIG.  89. 


TT7  .  |,,1  U\  . 

W  ~~  v  "V   ~~T~  D  1)    1OP"  —  ^—  tr  V  1 

fit        I       f\\  O*  „.  f\       I    ' 

butp^  =P,Vt  for  an  isothermal  change,  and  consequently 

*L (340) 


456 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


Some  investigators  have  taken  the  work  of  isothermal 
compression,  represented  by  equation  (340),  as  a  basis  of 
comparison  for  compressors  and  have  considered  its  ratio  to 
the  actual  work  of  compression  as  the  efficiency  of  compres- 
sion. This  throws  together  into  one  factor  the  effect  of 
heating  during  compression  and  the  effect  of  imperfect  valve- 
action. 

Professor  Riedler*  obtained  indicator-diagrams  from  the 
cylinders  of  a  number  of  air-compressors  and  drew  upon  them 
the  diagrams  which  would  represent  the  work  of  isothermal 
compression,  without  clearance  or  valve  losses.  A  compari- 
son of  the  areas  of  the  isothermal  and  the  actual  diagrams 
gave  the  arbitrary  efficiency  of  compression  just  described. 
The  following  table  gives  his  results: 

ARBITRARY    EFFICIENCY   OF   COMPRESSION. 


Type  of  compressor. 

Pressures  in 
•main, 
atmospheres. 

Lost  work  in 
per  cent  of 
useful  work. 

Arbitrary 
efficiency. 

6 

105  o 

o  488 

do                       

6 

Q2  .O 

o  521 

Colladon                                   •      •            .... 

V4-  J 
og     TC 

•  bo 

•  77* 

6 

4.2.  7 

o  701 

Cockerill                     

6 

AQ     O 

Riedler  two-stacre   

6 

12    O7 

A  similar  comparison  for  a  fluid  piston-compressor  showed 
an  efficiency  of  0.84. 

There  are  three  notable  conclusions  that  may  be  drawn 
from  this  table:  (i)  there  is  much  difference  between  com- 
pressors working  at  the  same  pressures,  (2)  a  simple  com- 
pressor loses  efficiency  rapidly  as  the  pressure  rises,  and  (3) 
the  compound  or  two-stage  compressor  shows  a  great  advan- 
tage over  a  simple  compressor. 


*  Development  and  Distribution  of  Power,  Unwin. 


COMPRESSED   AIR.  457 

Test  of  a  Blowing-engine. — Pernolet*  gives  the  follow- 
ing test  of  a  blowing-engine  used  to  produce  the  blast  for 
Bessemer  converters  at  Creusot.  The  engine  was  a  two- 
cylinder  horizontal  engine,  with  the  cranks  at  right  angles. 
The  piston-rod  for  each  cylinder  extended  through  the 
cylinder-head  and  actuated  a  double-acting  compressor. 
The  dimensions  were: 

Diameter,  steam-pistons 1.2  metres. 

"          air-pistons 1.5        " 

Stroke. 1.8 

Diameter  of  fly-wheel 8.0 

At  28  revolutions  per  minute  the  following  results  were 
obtained : 

Indicated  horse-power  of  steam-cylinders. .    . .   1082 
"  "  "  air-cylinders 999 

Efficiency 0.92 

Temperature  of  air  admitted 10°  C. 

"    "    delivered 60°  C. 

Pressure  of   air  delivered,  metres  of  mercury 

above  the  atmosphere 1.21 

Pressure  of  air  in  supply-pipe,  metres  of  mer- 
cury below  the  atmosphere 0.023 

At  25  revolutions  there  was  no  sensible  depression  of 
pressure  in  the  supply-pipe. 

The  air  from  such  a  blowing-engine  probably  suffers  little 
loss  of  temperature  after  compression. 

Air-pumps. — The  feed-water  supplied  to  a  steam-boiler 
usually  contains  air  in  solution,  which  passes  from  the  boiler 
with  the  steam  to  the  engine  and  thence  to  the  condenser. 
In  like  manner  the  injection-water  supplied  to  a  jet-condenser 
brings  in  air  in  solution.  Also  there  is  more  or  less  leakage 
of  air  into  the  cylinder  communicating  with  the  condenser 

*  L! Air  Comprim/,  1876. 


458  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

and  into  the  exhaust-pipe  or  the  condenser  itself.  An  air- 
pump  must  therefore  be  provided  to  remove  this  air  and  to 
maintain  the  vacuum.  The  air-pump  also  removes  the  con- 
densed steam  from  a  surface-condenser,  and  the  mingled 
condensed  steam  and  injection-water  from  a  jet-condenser. 
If  no  air  were  brought  into  the  condenser  the  vacuum  would 
be  maintained  by  the  condensation  of  the  steam  by  the 
injection,  or  the  cooling  water,  and  it  would  be  sufficient  to 
remove  the  water  by  a  common  pump,  which,  with  a  surface- 
condenser,  might  be  the  feed-pump. 

The  weight  of  injection-water  per  pound  of  steam,  calcu- 
lated by  the  method  on  page  250,  will  usually  be  less  than  20 
pounds,  but  it  is  customary  to  provide  30  pounds  of  injection- 
water  per  pound  of  steam,  with  some  method  of  regulating 
the  quantity  delivered. 

It  may  be  assumed  that  the  injection-water  will  bring  in 
with  it  one-twentieth  of  its  volume  of  air  at  atmospheric 
pressure,  and  that  this  air  will  expand  in  the  condenser  to  a 
volume  inversely  proportional  to  the  absolute  pressure  in  the 
condenser.  The  capacity  of  the  air-pump  must  be  sufficient 
to  remove  this  air  and  the  condensed  steam  and  injection- 
water. 

An  air-pump  for  use  with  a'  surface-condenser  may  be 
smaller  than  one  used  with  a  jet-condenser.  In  marine  work 
it  is  common  to  provide  a  method  of  changing  a  surface-  into 
a  jet-condenser,  and  to  make  the  air-pump  large  enough  to 
give  a  fair  vacuum  in  case  such  a  change  should  become 
advisable  in  an  emergency. 

Seaton  *  states  that  the  efficiency  of  a  vertical  single- 
acting  air-pump  varies  from  0.4  to  0.6,  and  that  pf  a  double- 
acting  horizontal  air-pump  from  0.3  to  0.5,  depending  on  the 
design  and  condition ;  that  is,  the  volume  of  air  and  water 
actually  discharged  will  bear  such  ratios  to  the  displacement 
of  the  pump. 

*  Manual  of  Marine  Engineering. 


COMPRESSED   A  IK. 


459 


He  also  gives  the  following  table  of  ratios  of  capacity  of 
air-pump  cylinders  to  the  volume  of  the  engine  cylinder  or 
cylinders  discharging  steam  into  the  condenser: 

RATIO    OF    ENGINE   AND   AIR-PUMP   CYLINDERS. 


Description  of  pump. 

Description  of   engine. 

Ratio. 

Double 

actin    vertical 

Jet-conden 
Surface- 
Jei- 
Surface- 

Jet-conden 
Surface- 
Jet- 

Surface- 
« 

sing,  expansion  i£  to  2 
i|  to  2 
3  to  5 
3  to  5 
compound. 

6  to    8 
8  to  10 

10  to  12 

12  to  15 
15  to  18 
10  to  13 
13  to  16 
16  to  19 
19  to  24 
24  to  28 

8       .< 

« 

M 

« 

-acting  horizontal 

<                                                    4  < 
<                                                    « 

ing,  expansion   i£  to  2 
i£  to  2 
3  to  5 
3  to  5 
compound..  

Calculation  for  an  Air-compressor.  —  Let  it  be  required 
to  find  the  dimensions  of  an  air-compressor  to  deliver  300 
cubic  feet  of  air  per  minute  at  100  pounds  per  square  inch  by 
the  gauge,  and  also  the  horse-power  required  to  drive  it. 

If  it  is  assumed  that  the  air  is  forced  into  the  delivery- 
pipe  at  the  temperature  of  the  atmosphere,  and,  further,  that 
there  is  no  loss  of  pressure  between  the  compressor  and  the 
delivery-pipe,  equation  (318)  for  finding  the  volume  drawn 
into  the  compressor  will  be  reduced  to 


=  300  X 


=  2341  cubic  feet. 


If  now  we  allow  five  per  cent  for  imperfect  valve-action 
and  for  heating  the  air  as  it  is  drawn  into  the  compressor  the 
apparent  capacity  of  the  compressor  will  be 

2341-7-  0.95  =  2464  cubic  feet  ; 

this  is  the  volume  on  which  the  power  for  the  compressor 
must  be  calculated. 

If  the  clearance  of  the  compressor  is  0.02  of  the  piston 


r  3  -> 

460  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

displacement,  then  the  factor  for  allowing  for  clearance  will 
be 


= 


m\p  m  100  \i4-7     /       100 


if  the  exponent  of  the  equation  representing  the  expansion  of 
the  air  in  the  clearance  is  1.4.  Consequently  the  volume 

on  which  the  dimensions  of  the  compressor  must  be  based  is 

//ty 

2464  ~  0.9332  =  2640  cubic  feet. 

At  80  revolutions  per  minute  the  mean  piston  displacement 
will  be 

2640  -f-  (2  X  80)  =  16.5  cubic  feet. 

Assuming  a  stroke  of  3  feet,  the  mean  area  of  the  piston 
must  be 

(144  X  16.5)  -r-  3  =  792  square  inches. 

Allowing  1  6  square  inches  for  a  piston-rod  4^  inches  in 
diameter  gives  a  mean  area  of  800  square  inches  for  the 
piston,  which  corresponds  very  nearly  to  32  inches  for  the 
diameter  of  the  piston. 

The  power  expended  in  the  compressor-cylinder  may  be 
calculated  by  equation  (315),  using  for  F,  the  apparent 
capacity  of  the  compressor,  giving 


H.  P.  = 


144  X  147  X  2464  X  1.4 


X  147  X  2404  X  1.4  (  /ii47>"TT"    _     } 
33000  X  (1.4  -  i)        ft  14.77  ^-442. 


If  the  friction  of  the  combined  steam-engine  and  com- 
pressor is  assumed  to  be  15  per  cent  the  horse-power  of  the 
steam-cylinder  must  be 

442  ~  0.85  =  520. 
If  the   temperature   of    the   atmosphere    drawn   into   the 


COMPRESSED    AIR.  461 

compressor  is  70°  F.,  then  by  an  equation  like  (80),  page  67, 
the  delivery  temperature  will  be 


T,  =  Tt  =  (460.7  +  70)  =  954°.4 


absolute,  or  about  494°  F. 

The  calculation  has  been  carried  on  for  a  simple  com- 
pressor, but  there  will  be  a  decided  advantage  in  using  a 
compound  compressor  for  such  work.  Such  a  compressor 
should  have  for  the  pressure  in  the  intermediate  reservoir 


P'  =  ^AA  =  Vii4.7  X  14-7  =  4i.o6  pounds. 


The  factor  for  allowing  for  clearance  of  the  low-pressure 
cylinder  will  now  be 


m  100x14.7;          100 

The  loss  from  imperfect  action  of  the  valves  and  for  heat- 
ing of  the  air  as  it  enters  the  compressor  will  be  less  for  a 
compound  than  for  a  simple  compressor,  but  we  will  here 
retain  the  value  2464  cubic  feet,  previously  found  for  the 
apparent  capacity  of  the  compressor.  The  volume  from  which 
the  dimensions  of  the  condenser  will  be  found  will  now  be 

2464  -r-  0.9784  =2518  cubic  feet, 

which  with  80  revolutions  per  minute  will  give  15.74  cubic 
feet  for  the  piston  displacement,  and  755.5  square  inches  for 
the  effective  piston  area,  if  the  stroke  is  made  3  feet,  as 
before.  Adding  16  inches  for  the  piston-rod,  which  will  be 
assumed  to  pass  entirely  through  the  cylinder,  will  give  for 
the  diameter  of  the  low-pressure  cylinder  3  if  inches. 

Since  the  pressure  p'  is  a  mean  proportional  between  /, 
and  /„  the  clearance  factor  for  the  high-pressure  cylinder  will 
be  the  same  as  that  for  the  low-pressure  cylinder,  and,  as  the 


462  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

volumes  are  inversely  proportional  to  the  pressures  p^  and/', 
the  high-pressure  piston  displacement  will  be 

(15.74  X  14.7)  -r-  41.06  =  5.64  cubic  feet. 

If  we  allow  8  inches  for  a  rod  4^-  inches  in  diameter  at  one 
side  of  the  piston,  then  the  mean  area  of  the  piston  will  be 
278.7  square  inches,  which  corresponds  to  a  diameter  of  i8J 
inches  for  the  high-pressure  cylinder.  In  reality  the  piston- 
rod  for  the  compound  compressor  may  have  a  less  diameter 
than  the  rod  for  a  simple  compressor,  because  the  maximum 
pressure  on  both  pistons  will  be  less  than  that  for  the  piston 
of  the  simple  compressor.  Again,  the  rod  which  extends 
from  the  large  to  the  small  piston  may  be  reduced  in  size. 
But  details  like  these  which  depend  on  the  calculation  of 
strength  cannot  properly  receive  much  attention  at  this  place. 
The  power  required  to  drive  the  compressor  may  be 
derived  from  equation  (236),  replacing  ^,,  the  specific  volume, 
by  Fj,  the  apparent  capacity  of  the  low-pressure  cylinder. 
Using  the  apparent  capacity  already  obtained,  2464  cubic 
feet,  we  have  for  the  power  expended  in  the  air-cylinders 

H  p  _2  X  144  X  147  X  2464  X  1.4  (  /4£f<V^r_     ) 

33000  X  (1.4-  i)  UH.7J  I[-377; 

and,  as  before,  allowing  15  per  cent  for  friction  of  the  engine 
and  compressor,  we  have  for  the  indicated  horse-power  of  the 
steam-engine 

377^0.85  =444- 

The  temperature  at  the  delivery  from  the    low-pressure 
cylinder  will  be  for  70°  F.  atmospheric  temperature 


absolute,  or  25  i°  F.  Since  /'  is  a  mean  proportional  between 
pl  and  /3,  this  will  also  be  the  temperature  of  the  air  delivered 
by  the  high-pressure  cylinder. 


COMPRESSED   AIR.  463 

Friction  of  Air  in  Pipes.  —  The  resistance  to  the  flow  of  a 
liquid  through  a  pipe  is  represented  in  works  on  hydraulics 
by  an  expression  having  the  form 


In  which  C  is  an  experimental  coefficient,  u  is  the  velocity  in 
feet  per  second,  g  is  the  acceleration  due  to  gravity,  /  is  the 
length  of  the  pipe  in  feet,  and  m  is  the  hydraulic  mean  depth, 
which  last  term  is  obtained  by  dividing  the  area  of  the  pipe 
by  its  perimeter.  For  a  cylindrical  pipe  we  have  consequently 


m-  =  \7td*  -r-  nd  =  \d.  .....     (342) 

The  expression  represents  the  head  of  liquid  required  to 
overcome  the  resistance  of  friction  in  the  pipe  when  the 
velocity  of  flow  is  u  feet  per  second.  Such  an  expression 
cannot  properly  be  applied  to  flow  of  air  through  a  pipe  when 
there  is  an  appreciable  loss  of  pressure,  for  the  accompanying 
increase  in  volume  necessitates  an  increase  of  velocity,  whereas 
the  expression  treats  the  velocity  as  a  constant.  If,  however, 
we  consider  the  flow  through  an  infinitesimal  length  of  pipe, 
for  which  the  velocity  may  be  treated  as  constant,  we  may 
write  for  the  loss  of  head  due  to  friction 

*  M 
^gm  ........     (343) 

This  loss  of  head  is  the  vertical  distance  through  which  the 
air  must  fall  to  produce  the  work  expended  in  overcoming 
friction,  and  the  total  work  thus  expended  may  be  found  by 
multiplying  the  loss  of  head  by  the  weight  of  air  flowing 
through  the  pipe.  It  is  convenient  to  deal  with  one  pound 
of  air,  so  that  the  expression  for  the  loss  of  head  also  repre- 
sents the  work  expended. 

The  air  flowing  through  a  long  pipe  soon  attains  the  tem- 
perature of  the  pipe  and  thereafter  remains  at  a  constant 
temperature,  so  that  our  discussion  for  the  resistance  of  fric- 


464  THERMODYNAMICS  OF   THE   STEAM-ENGINE. 

tion  may  be  made  under  the  assumption  of  constant  tempera- 
ture, which  much  simplifies  our  work,  because  the  intrinsic 
energy  of  the  air  remains  constant.  Again,  the  work  done  by 
the  air  on  entering  a  given  length  dl  will  be  equal  to  the 
work  done  by  the  air  when  it  leaves  that  section,  because  the 
product  of  the  pressure  by  the  volume  is  constant. 

Since  there  is  a  continual  increase  of  volume  corresponding 
to  the  loss  of  pressure  to  overcome  friction,  and  consequently 
a  continual  increase  of  velocity  from  the  entrance  to  the  exit 
end  of  the  pipe,  there  is  also  a  continual  gain  of  kinetic 
energy.  But  the  velocity  of  air  in  long  pipes  is  small  and  the 
changes  of  kinetic  energy  can  be  neglected. 

The  air  expands  by  the  amount  dv  as  it  passes  through 
the  length  dl  of  pipe,  and  each  pound  does  the  work  pdv. 
This  work  must  be  supplied  by  the  loss  of  head,  and,  since 
there  is  no  other  expenditure  of  energy,  the  work  expended 
in  the  loss  of  head  is  equal  to  the  work  done  by  expansion; 
consequently 

pdv  =  C •     (343) 

2gm 

But  from  the  characteristic  equation 

(344) 


we  have 


RT  1 
dv=-  —dp, 


which  substituted  in  equation  (343)  gives 
«'  dl  RT  , 

cv'*  =  ~T"  A    •  *  '  '  '  (345) 

If  the  area  of  the  pipe  is  A  square  feet,  and  if  W  pounds 
of  air  flow  through  it  per  second,  then 

Wv        WRT 


COMPRESSED   AIR,  465 

in  which  v  is  the  specific  volume,  for  which  a  value  may  be 
derived  from  equation  (344).  Replacing  u  in  equation  (345) 
by  the  value  just  derived,  we  have 

l  RT 


dl  p 

=--dp  .....     (347) 


Integrating  between  the  limits  L  and  o,  and/,  and/,,  we 
have 


But  from  equation  (346)  the  velocity  at  the  entrance  to  the 
pipe  where  the  pressure  is  /,  will  be 

WRT 


so  that  equation  (348)  may  be  reduced  to 

A£*;L_  _/.'-A\ 

~       RT 


Equation  (349  may  be  solved  as  follows: 

.     .     .     .     (35o> 

....     (351) 


gRTm] 

£  <5""~  •*• 


The  first  two  forms  allow  us  to  calculate  either  the  velocity 
or  the  loss  of  pressure;  the  last  form  may  be  used  to  calcu- 
late values  of  C  from  experiments  on  the  flow  through  pipes- 


466          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

From  experiments  made  by  Riedler  and  Gutermuth* 
Professor  Unwin  f  deduces  the  following  values  for  £: 

Diameter  of  pipe,  feet.  C 

0.492  0.00435 

0.656  0.00393 

0.980  0.00351 

For  pipes  over  one  foot  in  diameter  he  recommends  for  use 

C  =  0.003. 

Replacing  the  hydraulic  mean  depth  m  by  \d,  its  value 
for  round  pipes,  and  using  R  =  53.22  and  g  =  32.  16,  we  have 
in  place  of  equation  (351) 

C»,'£    )  * 
>•='•{  '"i^r  ......    (353) 

All  of  the  dimensions  are  given  in  feet,  but  from  the  form 
of  the  equation  it  is  evident  that  the  pressures  may  be  in  any 
convenient  units,  for  example,  in  pounds  per  square  inch 
absolute. 

For  example,  let  us  find  the  loss  of  pressure  of  300  cubic 
feet  per  minute  if  delivered  through  a  six-inch  pipe  a  mile 
long,  the  initial  pressure  being  100  pounds  by  the  gauge. 

The  velocity  of  the  air  will  be 


(300*  60)-^  =  5  ^  =  25.5  feet. 

The  terminal  pressure  will  consequently  be 

0.0044  X  25^5  2  X  5280  )  * 


•  (          0.0044  X  255    X  520  ) 

430(460.7+70)*  t 

=  106.8  pounds, 


*  Neue  Erfahrungen  iiber  die  Kraftversorgung  von  Paris  durch  Druck- 
luft,  1891. 

^Development  and  Distribution  of  Power. 


u  JN  l  V  i^RSITY 


COMPRESSED   AIR. 


467 


with  70°  F.  for  the  temperature  of  the  atmosphere  and  with 
C  =  0.0044.  Consequently  the  loss  of  pressure  is  about  eight 
pounds. 

Compressed-air  Engines.  —  Engines  for  using  com- 
pressed air  differ  from  steam-engines  only  in  details  that 
depend  on  the  nature  of  the  working  fluid.  In  some  instances 
compressed  air  has  been  used  in  steam-engines  without  any 
change;  for  example,  in  Fig.  90  the  dotted  diagram  was 


FIG.  90. 

taken  from  the  cylinder  of  an  engine  using  compressed  air, 
and  the  dot-and-dash  diagram  was  taken  from  the  same  end 
of  the  cylinder  when  steam  was  used  in  it.  The  full  line  ab 
is  a  hyperbola  and  the  line  ac  is  the  adiabatic  line  for  a  gas; 
both  lines  are  drawn  through  the  intersection  of  the  expansion 
lines  of  the  two  diagrams. 

Power  of  Compressed-air  Engines.  —  The  probable 
mean  effective  pressure  attained  in  the  cylinder  of  a  com- 
pressed-air engine,  or  to  be  expected  in  a 
projected  engine,  may  be  found  in  the  same 
manner  as  is  used  in  designing  a  steam- 
engine.  In  Fig.  91  the  expansion  curve 
i  2  and  the  compression  curve  3  o  may  be 
assumed  to  be  adiabatic  lines  for  a  gas 
represented  by  the  equation 


FIG.  91.; 


and  the  area  of  the  diagram  may  be  found  in  the  usual  way, 
and  therefrom  the  mean  effective  pressure  can  be  determined. 


468  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

Having  the  mean  effective  pressure,  the  power  of  a  given 
engine  or  the  size  required  for  a  given  power  may  be  deter- 
mined directly.  The  method  will  be  illustrated  later  by  an 
example. 

Air-consumption. — The  air  consumed  by  a  given  com- 
pressed-air engine  may  be  calculated  from  the  volume, 
pressure,  and  temperature  at  cut-off  or  release,  and  the 
volume,  temperature,  and  pressure  at  compression,  in  the 
same  way  that  the  indicated  consumption  of  a  steam-engine 
is  calculated ;  but  in  this  case  the  indicated  and  actual  con- 
sumption should  be  the  same,  since  there  is  no  change  of 
state  of  the  working  fluid.  Since  the  intrinsic  energy  of  a 
gas  is  a  function  of  the  temperature  only,  the  temperature 
will  not  be  changed  by  loss  of  pressure  in  the  valves  and 
passages,  and  the  air  at  cut-off  will  be  cooler  than  in  the 
supply-pipe,  only  on  account  of  the  chilling  action  of  the  walls 
of  the  cylinder  during  admission,  which  action  cannot  be 
energetic  when  the  air  is  dry,  and  probably  is  not  very  im- 
portant when  the  air  is  saturated. 

Final  Temperature. — If  the  expansion  in  a  compressed- 
air  engine  is  complete,  i.e.,  if  it  is  carried  down  to  the  pres- 
sure in  the  exhaust-pipe,  then,  assuming  that  there  are  ns> 
losses  of  pressure  in  valves  and  passages,  the  final  temperature 
may  be  found  by  the  equation 


(354) 


If  the  expansion  is  not  complete,  then  the  temperature  at 
the  end  of  expansion  may  be  found  by  the  equation 


(355) 


in  which  Vc  is  the  volume  in  the  cylinder  at  cut-off  and  Vr  at 
release,  Tr  is  the  absolute  temperature  at  the  end  of  expan- 
sion, and  7",  is  the  temperature  at  cut-off,  assumed  to  be  the 


COMPRESSED   AIR.  469 

same  as  in  the  supply-pipe.  Tr  is  not  the  temperature  during 
back-pressure  nor  in  the  exhaust-pipe.  When  the  exhaust- 
valve  is  opened  at  release  the  air  will  expand  suddenly,  and 
part  of  the  air  will  be  expelled  at  the  expense  of  the  energy 
in  the  air  remaining — much  as  though  that  air  expanded 
behind  a  piston,  and  the  temperature  in  the  cylinder  during 
exhaust  and  at  the  beginning  of  compression  may  be  calcu- 
lated by  equation  (354).  The  temperature  in  the  exhaust- 
pipe  will  not  be  so  low,  for  the  temperature  of  the  escaping 
air  will  vary  during  the  expulsion  produced  by  sudden  expan- 
sion, and  will  only  at  the  end  of  that  operation  have  the 
temperature  Tt,  while  the  energy  expended  on  that  air  to 
give  it  velocity  will  be  restored  when  the  velocity  is  reduced 
to  that  in  the  exhaust  pipe. 

Volume  of  the  Cylinder.  — The  determination  of  the 
volume  of  the  cylinder  of  a  compressed-air  engine  which  uses 
a  stated  volume  of  air  per  minute  is  the  converse  of  the 
determination  of  the  air  consumed  by  a  given  engine,  and  can 
be  found  by  a  similar  process.  We  may  calculate  the  volume 
of  air,  at  the  pressure  in  the  supply-pipe,  consumed  per  stroke 
by  an  engine  having  one  unit  of  volume  for  its  piston  dis- 
placement, and  therefrom  find  the  number  of  units  of  volume 
of  the  piston  displacement  for  the  required  engine. 

Interchange  of  Heat. — The  interchanges  of  heat  between 
the  walls  of  the  cylinder  of  a  compressed-air  engine  and  the 
air  working  therein  are  of  the  same  sort  as  those  taking  place 
between  the  steam  and  the  walls  of  the  cylinder  of  a  steam- 
engine;  that  is  to  say,  the  walls  absorb  heat  during  admission 
and  compression,  if  the  latter  is  carried  to  a  considerable 
degree,  and  yield  heat  during  expansion  and  exhaust.  Since 
the  walls  of  the  cylinder  are  never  so  warm  as  the  entering 
air  nor  so  cold  as  the  air  exhausted,  the  walls  may  absorb 
heat  during  the  beginning  of  expansion  and  yield  heat  during 
the  beginning  of  compression. 

The  amount  of  interchange  of  heat  is  much  less  in  a  com- 
pressed-air engine  than  in  a  stearn-engine.  With  a  moderate 


4/O  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

expansion  the  interchanges  of  heat  between  dry  air  and  the 
walls  of  the  cylinder  are  insignificant.  Moisture  in  the  air 
increases  the  interchanges  in  a  marked  degree,  but  does  not 
make  them  so  large  that  they  need  be  considered  in  ordinary 
calculations. 

Moisture  in  the  Cylinder. — The  chief  disadvantage  in  the 
use  of  moist  compressed  air — and  it  is  fair  to  assume  that 
compressed  air  is  nearly  if  not  quite  saturated  when  it  comes 
to  the  engine — is  that  the  low  temperature  experienced  when 
the  range  of  pressures  is  considerable  causes  the  moisture  to 
freeze  in  the  cylinder  and  clog  the  exhaust-valves.  The 
difficulty  may  be  overcome  in  part  by  making  the  valves  and 
passages  of  large  size.  Freezing  of  the  moisture  may  be  pre- 
vented by  injecting  steam  or  hot  water  into  the  supply-pipe 
or  the  cylinder,  or  the  air  may  be  heated  by  passing  it  through 
externally  heated  pipes  or  by  some  similar  device.  In  the 
application  of  compressed  air  to  driving  street-cars  the  air 
from  the  reservoir  has  been  passed  through  hot  water,  and 
thereby  made  to  take  up  enough  hot  moisture  to  prevent 
freezing.  The  study  of  gas-engines  suggests  a  method  of 
heating  compressed  air  which  it  is  believed  has  never  been 
tried.  The  air  supplied  to  a  compressed-air  engine,  or  a  part 
of  the  air,  could  be  caused  to  pass  through  a  lamp  of  proper 
construction  to  give  complete  combustion,  and  the  products 
of  combustion  passed  to  the  engine  with  the  air.  Should 
such  a  device  be  used  it  would  be  advisable  that  the  tem- 
perature of  the  air  should  be  raised  only  to  a  moderate  degree 
to  avoid  destruction  of  the  lubricants  in  the  cylinder,  and  the 
combustion  at  all  hazards  must  be  complete,  or  the  cylinder 
would  be  fouled  by  unburned  carbon. 

Compound  Air-engines. — When  air  is  expanded  to  a  con- 
siderable degree  in  a  compressed-air  engine  a  gain  may  be 
realized  by  dividing  the  expansion  into  two  or  more  stages  in 
as  many  cylinders,  provided  that  the  air  can  be  economically 
reheated  between  the  cylinders.  The  heat  of  the  atmosphere 
or  of  water  at  the  same  temperature  may  sometimes  be  used 


COMPRESSED    AIR.  4/1 

for  this  purpose.  It  is  not  known  that  machines  of  this  con- 
struction have  been  used.  If  they  were  to  be  constructed 
the  practical  advantages  of  equal  distribution  of  work  and 
pressure  would  probably  control  the  ratio  of  the  volumes  of 
the  cylinders. 

Calculation  for  a  Compressed-air  Engine.  —  Let  it  be 
required  to  find  the  dimensions  for  a  compressed-air  engine  to 
develop  100  indicated  horse-power  at  the  pressure  of  92 
pounds  by  the  gauge  and  at  70°  F.  Assume  the  clearance  to 
be  five  per  cent  of  the  piston  displacement,  and  assume  the 
cut-off  to  be  at  half  stroke,  the  release  to  be  at  the  end  of 
the  stroke,  and  the  compression  at  one-tenth  of  the  stroke. 

If  the  piston  displacement  is  represented  by  D,  then  the 
volume  in  the  cylinder  at  cut-off  will  be  0.30^,  that  at 
release  will  be  1.05/2,  and  that  at  compression  will  be  o.  i$D. 
The  absolute  pressures  during  supply  and  exhaust  may  be 
assumed  to  be  106.7  and  14.7  pounds  per  square  inch.  The 
work  for  one  stroke  of  the  piston  will  be 

144  X  106.7  Xo.3oZ>(        /0.30V-*-') 
^=144X106.7x0.25/2  +  -  /c_l          -j'-l^J         [ 

144  X  14.7  X  0.15/2  (        /0.05V'4"1  ) 


-144X14.7X0.9/2- 

=  144/2(26.68  +  31.530  —  13.23  —  1.96)  =  144  X  43-02/2. 

The  corresponding  mean  effective  pressure  is  43.02  pounds 
per  square  inch.  If  the  engine  is  furnished  with  large  ports 
and  automatic  valve-gear  the  actual  mean  effective  pressure 
maybe  0.9  of  that  just  calculated,  or  38.7  pounds  per  square 
inch. 

For  a  piston  displacement  D  the  engine  will  develop  at 
150  revolutions  per  minute 

144  x  38.7/2  x  2  x  150  , 

^*       °    '     —  —  —  —  2-  horse-power  ; 
33000 


472  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and  conversely  to  develop  100  horse-power  the  piston  dis- 
placement must  be 

100  X  33000 

D  = -  =  1.974  cubic  feet, 

144  X  38-7  X  2  X  150 

and  with  a  stroke  of  2  feet  the  effective  area  of  the  piston 
will  be 

1.974  X  144-^-  2  =  142.1  square  inches. 

If  the  piston-rod  is  2  inches  in  diameter  it  will  have  an  area 
of  3.14  square  inches,  so  that  the  mean  area  of  the  piston  will 
be  143.7  square  inches,  corresponding  to  a  diameter  of  13^ 
inches. 

We  find,  consequently,  that  an  engine  developing  100 
horse-power  under  the  given  conditions  will  have  a  diameter 
of  13^  inches  and  a  stroke  of  2  feet,  provided  that  it  runs  at 
150  revolutions  per  minute. 

In  order  to  determine  the  amount  of  air  used  by  the 
engine  we  must  consider  that  the  air  caught  at  compression 
is  compressed  to  the  full  admission-pressure  of  106.7  pounds 
.absolute.  Part  of  this  compression  is  done  by  the  piston  and 
part  by  the  entering  air,  but  for  our  present  purpose  it  is 
immaterial  how  it  is  done.  The  volume  filled  by  air  at 
atmospheric  pressure  when  the  exhaust-valve  closes  (including 
clearance)  is  0.15  of  the  piston  displacement.  When  the 
pressure  is  increased  to  106.7  pounds  the  volume  will  be 
reduced  to 


of  the  piston  displacement.  The  volume  drawn  in  from  the 
supply-pipe  will  consequently  be 

0.25  -f-  0.05  —  0.017  =  0.283 

of  the  piston  displacement.  If  the  compression  occurred 
sufficiently  early  to  raise  the  pressure  to  that  in  the  supply- 
pipe  before  the  admission-valve  opened,  then  only  0.25  of  the 


COMPRESSED    AIR.  473 

piston  displacement  would  be  used  per  stroke  and  a  saving 
of  about  13  per  cent  would  be  attained;  in  such  case  the 
mean  effective  pressure  would  be  smaller  and  the  size  of  the 
cylinder  would  be  larger. 

The  air-consumption  for  the  engine  appears  to  be 

2  X  1 50  X  0.283  X  pist.  displ.  =  2  X  1 50  X  0.283  X  1 .974  =  167.6 

cubic  feet  per  minute.  The  actual  air-consumption  will  be 
somewhat  less  on  account  of  loss  of  pressure  in  the  valves  and 
passages;  it  may  be  fair  to  assume  160  cubic  feet  per  minute 
for  the  actual  consumption. 

In  order  to  make  one  complete  calculation  for  the  use  of 
compressed  air  for  transmitting  power  the  data  for  the  com- 
pressed-air engine  have  been  made  to  correspond  with  the 
results  of  calculations  for  an  air-compressor  on  page  459  and 
for  the  loss  of  pressure  in  a  pipe  on  page  466.  Since  there 
is  a  loss  of  pressure  in  flowing  through  the  pipe  at  constant 
temperature,  there  is  a  corresponding  increase  of  volume,  so 
that  the  pipe  delivers 

300  X  i  H-7  -5-  106.7  =  322.6 

cubic  feet  per  minute.  Our  calculation  for  the  air-consump- 
tion of  an  engine  to  deliver  100  horse-power  gives  about  160 
cubic  feet,  from  which  it  appears  that  the  system  of  com- 
pressor, conducting-pipe,  and  compressed-air  engine  should 
deliver 

100  X  322.6  -=-  160  =  200  -|-  horse-power. 

If  the  friction  of  the  compressed-air  engine  is  assumed  to 
be  ten  per  cent  the  power  delivered  by  it  to  the  main  shaft 
(or  to  the  machine  driven  directly  from  it)  will  be 

200  X  .9  =  1 80  horse-power. 

The  steam-power  required  to  drive  a  simple  compressor 
was  found  to  be  520  horse-power,  it  consequently  appears 
that 

180  -r-  520  =  0.34 


474  THERMODYNAMICS   OF   THE   SJ'EAM-ENGINE. 

of  the  indicated  steam-power  is  actually  obtained  for  doing 
work  from  the  entire  system  of  transmitting  power.  If, 
however,  a  compound  compressor  is  used,  then  the  indicated 
steam-power  is  444,  and  of  this 

1 80  -r-  444  =  0.40 

will  be  obtained  for  doing  work. 

If,  however,  we  consider  that  the  power  would  in  any  case 
be  developed  in  a  steam-engine,  and  that  the  transmission 
system  should  properly  include  only  the  compressor-cylinder, 
the  pipe,  and  the  compressed-air  engine,  then  our  basis  of 
comparison  will  be  the  indicated  power  of  the  compressor- 
cylinder.  For  the  simple  compressor  we  found  the  horse- 
power to  be  442,  which  gives  for  the  efficiency  of  transmission 

180  -^  442  =  0.41, 

while  the  compound  compressor  demanded  only  377  horse- 
power, giving  an  efficiency  of 

1 80  -f-  377  =  0.48. 

It  appeared  that  the  failure  to  obtain  complete  compression 
involved  a  loss  of  about  13  per  cent  in  the  air-consumption. 
It  may  then  be  assumed  that  with  complete  compression  our 
engine  could  deliver  200  horse-power  to  the  main  shaft  In 
that  case  the  efficiency  of  transmission  when  a  compound 
compressor  is  used  may  be  0.53. 

Efficiency  of  Compressed-air  Transmission. — The  pre- 
ceding calculation  exhibits  the  defect  of  compressed  air  as  a 
means  of  transmitting  power.  It  is  possible  that  somewhat 
better  results  may  be  obtained  by  a  better  choice  of  pressures 
or  proportions;  Professor  Unwin  estimates  that  when  used 
on  a  large  scale  from  0.44  too. 51  of  the  indicated  steam- 
power  may  be  realized  on  the  main  shaft  of  the  compressed- 
air  engine.  On  the  other  hand,  when  compressed  air  is  used 
in  small  motors,  and  especially  in  rock-drills  and  other  mining- 
machinery,  much  less  efficiency  may  be  expected. 


COMPRESSED   AIR.  475 

Experiments  made  by  M.  Graillot  *  of  the  Blanzy  mines 
showed  an  efficiency  of  from  22  to  32  per  cent.  Experiments 
made  by  Mr.  Daniel  at  Leeds  gave  an  efficiency  varying  from 
0.255  to  0.455,  witn  pressures  varying  from  2.75  atmos- 
pheres to  1.33  atmospheres.  An  experiment  made  by  Mr. 
Kraft  f  gave  an  efficiency  of  o.  137  for  a  small  machine,  using 
air  at  a  pressure  of  five  atmospheres  without  expansion. 

Compressed  air  has  been  used  for  transmitting  power  either 
where  power  for  compression  is  cheap  and  abundant,  or  where 
there  are  reasons  why  it  is  specially  desirable,  as  in  mining  and 
tunnelling.  It  is  now  used  to  a  considerable  extent  for  driving 
hand-tools,  such  as  drills,  chipping-chisels,  and  calking-tools,. 
in  machine-  and  boiler-shops,  and  in  shipyards.  It  is  also  used 
for  operating  cranes  and  other  machines  where,  power  is  used 
only  at  intervals,  so  that  the  condensation  of  steam  (when 
used  directly)  is  excessive,  and  where  hydraulic  power  is  liable 
to  give  trouble  from  freezing. 

Compressed  air  has  been  used  to  a  very  considerable  extent 
for  transmitting  power  in  Paris.  The  system  appears  to  be 
expensive  and  to  be  used  mainly  on  account  of  its  convenience 
for  delivering  small  powers  or  in  places  where  the  cold  exhaust 
can  be  used  for  refrigeration.  The  trouble  from  freezing  of 
moisture  in  the  cylinder  has  been  avoided  by  allowing  the 
air  to  flow  through  a  coil  of  pipe  which  is  heated  externally  by 
a  charcoal  fire.  Professor  Unwin  estimates  that  an  efficiency  of 
transmission  of  0.75  may  be  attained  under  favorable  condi- 
tions when  the  air  is  heated  near  the  compressor,  but  he  does 
not  include  the  cost  of  fuel  for  reheating  in  this  estimate. 

Storage  of  Power  by  Compressed  Air.  — Reservoirs  or 
cylinders  charged  with  compressed  air  have  been  used  to  store 
power  for  driving  street-cars.  A  system  developed  by  Mekar- 
ski  uses  air  at  350  to  450  pounds  per  square  inch  in  reservoirs 
having  a  capacity  of  75  cubic  feet.  The  car  also  carries  a  tank 


*  Pernolet,  L'Air  Comprim<?t  pp.  549t  55°. 

f  Revue  universelle  des  Mines ,  2  serie,  tome  vi. 


4/6  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

of  hot  water  at  a  temperature  of  about  350°  F.,  through  which 
the  air  passes  on  the  way  to  the  motor  and  by  which  it  is 
heated  and  charged  with  steam.  This  use  of  hot  water  gives 
a  secondary  method  of  storing  power  and  also  avoids  trouble 
from  freezing  in  the  motor-cylinders.  Air  at  much  higher 
pressures  has  been  used  for  driving  street-cars  in  New  York 
City,  but  the  particulars  have  not  been  given  to  the  public. 

The  calculation  for  storage  of  power  may  be  made  in  much 
the  same  way  as  that  for  the  transmission  of  power;  the  chief 
difference  is  due  to  the  fact  that  the  air  is  reduced  in  pressure 
by  passing  it  through  a  reducing-valve  on  the  way  from  the 
reservoir  to  the  motor.  By  the  theory  of  perfect  gases  such 
a  reduction  of  pressure  should  not  cause  any  change  of  tem- 
perature, but  the  experiments  of  Joule  and  Thomson  (page  72) 
show  that  there  will  be  an  appreciable,  though  not  an  impor- 
tant, loss  of  temperature  when  there  is  a  large  reduction  of 
pressure.  Thus  at  70°  F.  or  2i°.i  C.  the  loss  of  temperature 
for  each  100  inches  of  mercury  will  be 

°°'92  X  '  =  °°-79  C.  =  if  F. 


Now  100  inches  of  mercury  are  equivalent  to  about  49 
pounds  to  the  square  inch,  so  that  100  pounds  difference  of 
pressure  will  give  about  3^°  F.  reduction  of  temperature  and 
1000  pounds  difference  of  pressure  will  give  about  35°  F.  re- 
duction of  temperature.  The  last  figures  are  far  beyond  the 
limits  of  the  experiments  and  the  results  are  therefore  crude. 
Again,  the  air  in  passing  through  the  reducing-valve  and  the 
piping  beyond  will  gain  heat  and  consequently  show  a  smaller 
reduction  of  temperature.  The  whole  subject  of  loss  of 
temperature  due  to  throttling  is  more  curious  than  useful  and 
need  not  be  considered  in  practical  calculations. 

For  an  example  of  the  calculation  for  storage  of  power  let 
us  find  the  work  required  to  store  air  at  450  pounds  per  square 
inch  in  a  reservoir  containing  75  cubic  feet.  Replacing  the 
specific  volume  z>,  in  equation  (339)  by  the  actual  volume,  we 


COMPRESSED   AIR.  477 

have  for  the  work  of  compression  (not  allowing  for  losses  and 
imperfections) 


=  649300  foot-pounds. 

If  the  pressure  is  reduced  to  50  pounds   by  the   gauge  before 
it  is  used  the  volume  of  air  will  be 

75  x  464-7  -H  64.7  =  539  cubic  feet. 

The  work  for  complete  expansion  of  one  pound  to  the  pressure 
of  the  atmosphere  will  be 


and  the  work  for  539  cubic  feet  will  be 

1  ~  =  4873°°       ' 


51.4  -  T    \ 
1  ~  (§$    "'     \  = 


foot-pounds,  without  allowing  for  losses  or  imperfections. 
The  maximum  efficiency  of  storing  and  restoring  energy  by 
the  use  of  compressed  air  in  this  case  is  therefore 

487300  ^  649300  =  0.75. 

In  practice  the  efficiency  cannot  be  more  than  0.50,  if 
indeed  it  is  so  high. 

It  may  not  be  out  of  place  to  call  attention  to  a  danger 
that  may  arise  if  air  at  high  pressure  is  suddenly  let  into  a 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

pipe  which  has  oil  mingled  with  the  air  in  it  or  even  adher- 
ing to  the  side  of  the  pipe.  The  air  in  the  pipe  will  be  com- 
pressed and  its  temperature  may  become  high  enough  to 
ignite  the  oil  and  cause  an  explosion.  That  this  danger  is 
not  imaginary  is  shown  by  an  explosion  which  occurred  under 
such  conditions  in  a  pipe  which  was  strong  enough  to  with- 
stand the  air-pressure. 


CHAPTER  XVIII. 
REFRIGERATING-MACHINES. 

A  REFRIGERATING-MACHINE  is  a  device  for  producing  low 
temperatures  or  for  cooling  some  substance  or  space.  It  may 
be  used  for  making  ice  or  for  maintaining  a  low  temperature 
in  a  cellar  or  storehouse. 

Refrigeration  on  a  small  scale  may  be  obtained  by  the 
solution  of  certain  salts ;  a  familiar  illustration  is  the  solution 
of  common  salt  with  ice,  another  is  the  solution  of  sal  am- 
moniac in  water.  Certain  refrigerating-machines  depend  on 
the  rapid  absorption  of  some  volatile  liquid,  for  example,  of 
ammonia  by  water;  if  the  machine  is  to  work  continuously 
there  must  be  some  arrangement  for  redistilling  the  liquid 
from  the  absorbent.  The  most  recent  and  powerful  refriger- 
ating-machines are  reversed  heat-engines.  They  withdraw 
the  working  substance  (air  or  ammonia)  from  the  cold-room 
or  cooling-coil,  compress  it,  and  deliver  it  to  a  cooler  or  con- 
denser. Thus  they  take  heat  from  a  cold  substance,  do  work 
and  add  heat,  and  finally  reject  the  sum  of  the  heat  drawn  in 
and  the  heat  equivalent  of  the  work  done.  These  reversed 
heat-engines,  however,  are  very  far  from  being  reversible 
engines,  not  only  on  account  of  imperfect  valve  action  and 
losses  of  pressure,  but  because  the  walls  of  the  compressor- 
cylinder  have  an  appreciable  effect  on  the  working  substance. 

Two  forms  of  refrigerating-machines  are  in  common  use, 
air  refrigerating-machines  and  ammonia  refrigerating-machines. 
Sometimes  sulphur  dioxide  or  some  other  volatile  fluid  is  used 
instead  of  ammonia. 

479 


480 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


Air  Refrigerating-machine. — The  general  arrangement 
of  an  air  refrigerating-machine  is  shown  by  Fig.  92.  It  con- 
sists of  a  compression-cylinder  A,  an  expansion-cylinder  B  of 
smaller  size,  and  a  cooler  C.  It  is  commonly  used  to  keep 
the  atmosphere  in  a  cold-storage  room  at  a  low  temperature, 
and  has  certain  advantages  for  this  purpose,  especially  on  ship- 
board. The  air  from  the  storage-room  comes  to  the  com- 
pressor at  or  about  freezing-point,  is  compressed  to  two  or 
three  atmospheres  and  delivered  to  the  cooler,  which  has  the 
same  form  as  a  surface-condenser,  with  cooling  water  entering 
at  e  and  leaving  at/.  The  diaphragm  mn  is  intended  to  im- 
prove the  circulation  of  the  cooling  water.  From  the  cooler 
the  air,  usually  somewhat  warmer  than  the  atmosphere,  goes 
to  the  expansion-cylinder  By  in  which  it  is  expanded  nearly 


FIG.  92. 

to  the  pressure  of  the  air  and  cooled  to  a  low  temperature, 
and  then  delivered  to  the  storage-room.  The  inlet-valves 
a,  a  and  the  delivery-valves  b,  b  of  the  compressor  are  moved 
by  the  air  itself;  the  admission-valves  c,  c  and  the  exhaust- 
valves  dj  d  of  the  expansion-cylinder  are  like  those  of  a  steam- 
engine  and  must  be  moved  by  the  machine.  The  difference 
between  the  work  done  on  the  air  in  the  compressor  and  that 
done  by  the  air  in  the  expansion-cylinder,  together  with  the 
friction  work  of  the  whole  machine,  must  be  supplied  by  a 
steam-engine  or  other  motor. 


REFRIGERA  TING- MA  CHINES.  48 1 

It  is  customary  to  provide  the  compression-cylinder  with 
a  water-jacket  to  prevent  overheating,  and  frequently  a  spray 
of  water  is  thrown  into  the  cylinder  to  reduce  the  heating  and 
the  work  of  compression.  Sometimes  the  cooler  C,  Fig.  92, 
is  replaced  by  an  apparatus  resembling  a  steam-engine  jet-con- 
denser, in  which  the  air  is  cooled  by  a  spray  of  water.  In 
any  case  it  is  essential  that  the  moisture  in  the  air,  as  well  as 
the  water  injected,  should  be  efficiently  removed  before  the 
air  is  delivered  to  the  expansion-cylinder ;  otherwise  snow  will 
form  in  that  cylinder  and  interfere  with  the  action  of  the 
machine.  Various  mechanical  devices  have  been  used  to  col- 
lect and  remove  water  from  the  air,  but  air  may  be  saturated 
with  moisture  after  it  has  passed  such  a  device.  The  Bell- 
Coleman  Company  use  a  jet-cooler  with  provision  for  collect- 
ing and  withdrawing  water,  and  then  pass  the  air  through 
pipes  in  the  cold-room  on  the  way  to  the  expansion-cylinder. 
The  cold-room  is  maintained  at  a  temperature  a  little  above 
freezing-point,  so  that  the  moisture  in  the  air  is  condensed 
upon  the  sides  of  the  pipes  and  drains  back  into  the  cooler. 
The  same  machine  as  made  by  Menck  and  Hambrock  is  pro- 
vided with  a  device  for  removing  moisture  from  the  air  that 
is  shown  by  Fig.  93.  Air  from  the  cooler  comes  in  by  the 
pipe  a,  is  distributed  by  the  annular  perforated  pipe  b t  and 
passes  out  to  the  expansion-cylinder  by  the  pipe  c.  The 
chamber  E  is  surrounded  by  a  jacket  through  which  passes 
the  cold  air  on  the  way  from  the  expansion-cylinder  to  the 
cold-room.  Since  the  air  in  the  jacket  is  many  degrees  below 
freezing-point,  the  walls  of  the  chamber  E  are  quickly  covered 
with  frost,  which  accumulates  till  a  considerable  thickness  is 
attained ;  afterwards  the  moisture  condenses  and  runs  down 
to  the  bottom  of  the  chamber,  from  whence  it  is  withdrawn. 
A  coil  of  steam-pipe  dd  is  provided  for  thawing  ice  and  snow 
that  may  accumulate  at  the  bottom  of  the  chamber.  Since 
the  same  air  is  used  continuously,  being  taken  from  the  cold- 
room,  chilled,  and  returned,  the  effect  of  these  devices  is  to 
remove  the  moisture  from  the  air  in  the  cold-room  and  to 


482 


THERMODYNAMICS  OF   THE   STEAM-ENGINE. 


maintain  a  cold,  dry  atmosphere   in    it,  which  is  well  adapted 
to  preserving  all  kinds  of  perishable  provisions. 

When  an  air  refrigerating-machine  is  used  as  described  the 
pressure  in  the  cold-room  is  necessarily  that  of  the  atmos- 
phere, and  the  size  of  the  machine  is  large  as  compared  with 
its  performance.  The  performance  may  be  increased  by  run- 
ning the  machine  on  a  closed  cycle  with  higher  pressures ;  for 
^example,  the  cold  air  may  be  delivered  to  a  coil  of  pipe  in  a 


FIG.  93. 


non-freezing  salt  solution,  from  which  the  air  abstracts  heat 
through  the  walls  of  the  pipe  and  then  passes  to  the  com- 
pressor to  be  used  over  again.  The  machine  may  then  be  used 
to  produce  ice,  or  the  brine  may  be  used  for  cooling  spaces  or 
liquids.  A  machine  has  been  used  for  producing  ice  on  a 
small  scale,  without  cooling  water,  on  the  reverse  of  this  prin- 
ciple :  that  is,  atmospheric  air  is  first  expanded  and  chilled 
and  delivered  to  a  coil  of  pipe  in  a  salt  solution,  then  the  air 
is  drawn  from  this  coil,  after  absorbing  heat  from  the  brine, 
compressed  to  atmospheric  pressure,  and  expelled. 


REFRIGERA  TING- MA  CHINES.  48  3 

Proportion  of  Air  of  Refrigerating-machines. — The  per- 
formance of  a  refrigerating-machine  may  be  stated  in  terms 
of  the  number  of  thermal  units  withdrawn  in  a  unit  of  time, 
or  in  terms  of  the  weight  of  ice  produced.  The  latent  heat 
of  fusion  of  ice  may  be  taken  to  be  80  calories  or  144  B.  T.  U. 

Let  the  pressure  at  which  the  air  enters  the  compression- 
cylinder  be/!,  that  at  which  it  leaves  be/3;  let  the  pressure 
at  cut-off  in  the  expanding-cylinder  be/8  and  that  of  the  back- 
pressure in  the  same  be  p^ ;  let  the  temperatures  correspond- 
ing to  these  pressures  be  /,,  /,,  /3,  and  t^  or,  reckoned  from 
the  absolute  zero,  71,,  7",,  T3,  and  7"4.  With,  proper  valve- 
gear  and  large,  short  pipes  communicating  with  the  cold- 
chamber /4  may  be  assumed  to  be  equal  to/j  and  equal  to 
the  pressure  in  that  chamber.  Also  /,  may  be  assumed  to  be 
the  temperature  maintained  in  the  cold-chamber,  and  /,  may 
be  taken  to  be  the  temperature  of  the  air  leaving  the  cooler. 
With  a  good  cut-off  mechanism  and  large  passages  /3  may  be 
assumed  to  be  nearly  the  same  as  that  of  the  air  supplied  to 
the  expanding-cylinder.  Owing  to  the  resistance  to  the  pas- 
sage of  the  air  through  the  cooler  and  the  connecting  pipes 
and  passages,  /3  is  considerably  less  than  /,. 

It  is  essential  for  best  action  of  the  machine  that  the  ex- 
pansion and  compression  of  the  expanding-cylinder  shall  be 
complete.  The'  compression  may  be  made  complete  by  set- 
ting the  exhaust-valve  so  that  the  compression  shall  raise 
the  pressure  in  the  clearance-space  to  the  admission-pres- 
sure /,  at  the  instant  when  the  admission-valve  opens.  The 
expansion  can  be  made  complete  only  by  giving  correct 
proportions  to  the  expanding-  and  compression-cylinders. 

The  expansion  in  the  expanding-cylinder  may  be  assumed 
to  be  adiabatic,  so  that 


7",_/A\   « 

T,-\A) 


<>*> 


484  THERMODYNAMICS   OF   THE  STEAM-ENGINE. 

Were  the  compression  also  adiabatic  the  temperature  /3 
could  be  determined  in  a  similar  manner; 
but  the  air  is  usually  cooled  during  com- 
pression, and  contains  more  or  less  vapor,  so 
that  the  temperature  at  the  end  of  com- 


FIG.  94.  pression    cannot    be    determined    from     the 

pressure   alone,  even   though  the  equation   of  the  expansion 
curve  be  known. 

Let  the  air  passing  through  the  refrigerating-machine  per 
minute  be  M\  then  the  heat  withdrawn  from  the  cold-room  is 

<2,  =  Mcp(t,  -  /4)  ......     (357) 

The  work  of  compressing  M  pounds  of  air  from  the  pres- 
sure /,  to  the  pressure  /a  in  a  compressor  without  clearance  is 
(Fig.  94) 


We  =  JfLta  +   /    'pdv  -  pj>,  |  ; 

IS   7>2 


(358) 


provided  that  the  compression  curve  can  be  represented  by  an 
exponential  equation.  If  the  compression  can  be  assumed  to 
be  adiabatic 


-'-'*    (359) 


for  in  such  case  we  have  the  equations 


RE  FRIG  ERA  TING-MA  CHINES.  48  5 

If  the  expansion  is  complete  in  the  expanding-cylinder,  as 
should  always  be  the  case,  then  the  equation  for  the  work 
done  by  the  air  will  have  the  same  form  as  equation  (358)  or 
(359),  replacing  /,  and/  by  /4  and/4,  and  /,  and/,  by  /,  and 
/3  ;  so  that 


and  for  adiabatic  expansion 


The  difference  between  the  works  of  compression  and  ex- 
pansion is  the  net  work  required  for  producing  refrigeration ; 
consequently 

W  =  Wc—  We=  — ^j/,  —  /,  —  /,  -f-  /4};     .     (362) 
or,  replacing  M  by  its  value  from  equation  (357), 

w=¥'+l;r-C'' (363) 

The  net  horse-power  required  to  abstract  Q1  thermal  units 
per  minute  is  consequently 

^  =  7780,.  /.  +  /.-/.-, 
33000  *,-/. 

where  /,  is  the  temperature  of  the  air  drawn  into  the  com- 
pressor and  /,  is  the  temperature  of  the  air  forced  by  the  com- 
pressor into  the  cooler,  and  /,  is  the  temperature  of  the  air 
supplied  to  the  expanding-cylinder  and  /4  is  the  temperature 
of  the  cold  air  leaving  the  expanding-cylinder.  The  gross 
horse-power  developed  in  the  steam-engine  which  drives  the 
refrigerating-machine  is  likely  to  be  half  again  as  much  as  the 
net  horse-power  or  even  larger.  The  relation  of  the  gross 


486          THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and  the  net  horse-powers  for  any  air  refrigerating-machine 
may  readily  be  obtained  by  indicating  the  steam-  and  air- 
cylinders,  and  may  serve  as  a  basis  for  calculating  other 
machines. 

The  heat  carried  away  by  the  cooling  water  is 

Q,=  Qt  +  AW.     .     ..    .     .     .    (365) 

If  compression  and  expansion  are  adiabatic,  then 
<22  =  Mcp(t,  -  /,  +  ^  +  /4  -  />  -  /,)  =  Mcfa  -  /,)  ;      (366) 
or,  replacing  M  by  its  value  from  equation  (357), 

<2,=  e,!-^f    ••••••   (367) 

l\  —  t* 

If  the  initial  and  final  temperatures  of  the  cooling  water  are 
/,•  and  tk,  and  if  #,-  snd  9k  are  the  corresponding  heats  of  the 
liquid,  then  the  weight  of  cooling  water  per  minute  is 

G  =  —Q  __  Q  __  t"~  /3       -•     -     -      (368) 

ti-ik-    *fc  -O  («*-*<) 

The  compressor-cylinder  must  draw  in  M  pounds  of  air  per 
minute  at  the  pressure/),  and  the  temperature  t^  that  is,  with 
the  specific  volume  i\  ;  consequently  its  apparent  piston  dis- 
placement without  clearance  will  be,  at  N  revolutions  per 
minute, 


2N 

for  the  characteristic  equation  gives 


Replacing  M  by  its  value  from  equation  (357),  we  have 

(370) 


REFRIGERA  TING-  MA  CHINES. 

Since  all  the  air  delivered  by  the  compressor  must  pass 
through  the  expanding-cylinder,  its  apparent  piston  displace- 
ment will  be 

:     ;   •'•--•'  D.=  D&:    -;;.-:  vV   ;  "(37D 

If  ,  the  pressure  of  the  air  entering  the  compression-cylin- 
der, is  equal  to  /4,  that  of  the  air  leaving  the  expanding-cylin- 
der (as  may  be  nearly  true  with  large  and  direct  pipes  for  car- 
rying the  air  to  and  from  the  cold-room)  equation  (3/1)  will 
reduce  to 


(372) 


Both  the  compressor-  and  the  expanding-cylinder  will  have 
a  clearance,  that  of  the  expanding-cylinder  being  the  larger. 
As  is  shown  on  page  447,  the  piston  displacement  for  an  air- 
compressor  with  a  clearance  may  be  obtained  by  dividing  the 
apparent  piston  displacement  by  the  factor 


m\pj        m 

If  the  expansion  and  compression  of  the  expanding-cylin- 
der are  complete  the  same  factor  may  be  applied  to  it.  For 
a  refrigerating-machine  n  may  be  replaced  by  K  for  both  cyl- 
inders. To  allow  for  losses  of  pressure  and  for  imperfect 
valve  action  the  piston  displacements  for  both  compressor- 
and  expanding-cylinders  must  be  increased  by  an  amount 
which  must  be  determined  by  practice  ;  five  or  ten  per  cent 
increase  in  volume  will  probably  suffice.  In  practice  the  ex~ 
pansion  in  the  expanding-cylinder  is  seldom  complete.  A 
little  deficiency  at  this  part  of  the  diagram  will  not  have  a 
large  effect  on  the  capacity  of  the  machine,  and  will  prevent 
the  formation  of  a  loop  in  the  indicator-diagram  ;  but  a  large 
drop  at  the  release  of  the  expanding-cylinder  will  diminish 
both  the  capacity  and  the  efficiency  of  the  machine. 


488  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  temperature  t^  and  the  capacity  of  the  machine  may 
be  controlled  by  varying  the  cut-off  of  the  expanding-cylin- 
der.  If  the  cut-off  is  shortened  the  pressure  /3  will  be  in- 
creased, and  consequently  Tt  will  be  diminished.  This  will 
make  De,  the  piston  displacement  of  the  expanding-cylinder, 
smaller.  A  machine  should  be  designed  with  the  proper  pro- 
portions for  its  full  capacity,  and  then,  when  running  at  re- 
duced capacity,  the  expansion  in  the  expanding-cylinder  will 
not  be  quite  complete. 

Calculation  for  an  Air-compression  Machine.  —  Required 
the  dimensions  and  power  for  an  air  refrigerating-machine  to 
produce  an  effect  equal  to  the  melting  of  200  pounds  of  ice 
per  hour.  Let  the.  pressure  in  the  cold-chamber  be  14.7 
pounds  per  square  inch  and  the  temperature  32°  F.  Let  the 
pressure  of  the  air  delivered  by  the  compressor-cylinder  be 
39.4  pounds  by  the  gauge  or  55.1  pounds  absolute,  and  let 
there  be  ten  pounds  loss  of  pressure  due  to  the  resistance  of  the 
cooler  and  pipes  and  passages  between  the  compressor-  and 
the  expanding-cylinder.  Let  the  initial  and  final  temperatures 
of  the  cooling  water  be  60°  F.  and  80°  F.,  and  let  the 
temperature  of  the  air  coming  from  the  cooler  be  90°  F.  Let 
the  machine  make  60  revolutions  per  minute. 

With  adiabatic  expansion  and  compression  the  tempera- 
tures of  the  air  coming  from  the  compressor-  and  discharged 
from  the  expanding-cylinder  will  be 


=714.9; 


T4  =  460.7  +  90  t!±?\  w  =  402.3  ;          .-.      *,;<=-  58°. 
\44-  !/ 

The  melting  of  200  pounds  of  ice  is  equivalent  to 
200  X  144  -T-  60  =  480  B.  T.  u. 


REFRIGERA  TING-MA  CHINES.  489 

per  minute  ;  consequently  the  net  horse-power  of  the  machine 
is  by  equation  (364) 


P  - 


33000 


_^  778  x  480     254.2-  58.4-  32-90 

33000  32  +  58.4 

=  778  X  480  X  73.8  =  H    p 

33000  X  90.4 

and  the  indicated  power  of  the  steam-engine  may  be  assumed 
to  be  14  horse-power. 

By  equation  (370)  the  apparent  piston  displacement  of  the 
compressor  without  clearance  will  be 

Q'RT' 


480  X  53.22  X  49^7  __  =  2.33cu.  ft. 
2  X  60  X  0.2375  X  144  X  14-7  (32  +  58.4) 

By  equation  (372)  the  apparent  piston  displacement  of  the 
expanding-cylinder  without  clearance  will  be 


=  DC       =  2.33  x  =  1.90  cubic  feet 


If  the  clearance  of  the  compressor-cylinder  is  0.02  of  its 
piston  displacement,  then  the  factor  for  clearance  by  equation 
(316)  is 


so  that  the  piston  displacement  becomes 

2.33  -i.  0.979  =  2'38  cubic  feet, 


49° 


T HER  MOD  YNAMICS    OF   THE   STEAM-ENGINE. 


If,  further,  the  clearance  of  the  expander-cylinder  is  0.05 
of  its  piston  displacement  the  factor  for  clearance  becomes 


which  makes  the  piston  displacement 

1.90  -T-  0.963  =  1.97  cubic  feet. 

If  now  we  allow  ten  per  cent  for  imperfections  we  will 
get  for  the  dimensions:  stroke  2  feet,  diameter  of  the  com- 
pressor-cylinder 15^  inches,  and  diameter  of  the  expanding- 
cylinder  14  inches. 

Compression  Refrigerating-machine.  —  The  arrangement 
of  a  refrigerating-machine  using  a  volatile  liquid  and  its  vapor 
is  shown  by  Fig.  95.  The  essential  parts  are  the  compressor 
Ay  the  condenser  B,  the  valve  D,  and  the  vaporizer  C.  The 
compressor  draws  in  vapor  at  a  low  pressure  and  temperature, 
compresses  it,  and  delivers  it  to  the  condenser,  which  consists 
of  coils  of  pipe  surrounded  by  cooling  water  that  enters  at  c 


FIG.  95. 

and  leaves  at  f.     The  vapor  is  condensed,  and  the  resulting 
liquid  gathers  in  a  reservoir  in  the  bottom,  from  whence  it  is 


REFRIGERA  TING-  MA  CHINES.  49  1 

led  by  a  small  pipe  having  a  regulating-valve  D  to  the  vapor- 
izer or  refrigerator.  The  refrigerator  is  also  made  up  of  coils 
of  pipe,  in  which  the  volatile  liquid  vaporizes.  The  coils  may 
be  used  directly  for  cooling  spaces,  or  they  may  be  immersed 
in  a  tank  of  brine,  which  may  be  used  for  cooling  spaces  or  for 
making  ice.  Fig.  95  shows  the  compressor  with  one  single- 
acting  vertical  cylinder  which  has  head-valves,  foot-valves, 
and  valves  in  the  piston.  Single-acting  compressors  com- 
monly have  two  cylinders;  horizontal  compressors  usually 
have  one  double-acting  cylinder.  Some  vertical  compressors 
are  double-acting. 

The  cycle  which  has  been  stated  for  the  compression 
refrigerating-machine  is  incomplete,  because  the  working  fluid 
is  allowed  to  flow  through  the  expansion-cock  into  the  expand- 
ing-coils  without  doing  work.  To  make  the  cycle  complete 
there  should  be  a  small  expanding-cylinder  in  which  the  liquid 
could  do  work  on  the  way  from  the  condenser  to  the  vaporiz- 
ing-coils  ;  but  the  work  gained  in  such  a  cylinder  would  be 
insignificant,  and  it  would  lead  to  complications  and  diffi- 
culties. 

Proportions  of  Compression  Refrigerating-machines.— 
The  liquid  condensed  in  the  coils  of  the  condenser  flows  to  the 
expansion-cock  with  the  temperature  /,  and  has  in  it  the  heat 
q^  In  passing  through  the  expansion-cock  there  is  a  partial 
vaporization,  but  no  heat  is  gained  or  lost.  The  vapor  flow- 
ing from  the  expansion-coils  at  the  temperature  /2  and  the 
pressure  /,  is  usually  dry  and  saturated,  or  perhaps  slightly 
superheated,  as  it  approaches  the  compressor.  Each  pound 
consequently  carries  from  the  expanding-coils  the  total  heat  A,. 
Consequently  the  heat  withdrawn  from  the  expanding-coil 
by  a  machine  using  M  pounds  of  fluid  per  minute  is 

-?t)  ......     (374) 


The    compressor-cylinder   is    always    cooled    by  a  water- 
jacket,  but  it  is   not  probable  that  such  a  jacket  has  much 


492  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

effect  on  the  working  substance,  which  enters  the  cylinder  dry 
and  is  superheated  by  compression.  We  may  consequently 
calculate  the  temperature  of  the  vapor  delivered  by  the  com- 
pressor by  aid  of  equation  (181),  page  135,  giving 

k—L 

•    •     •     './,     •      (374) 

As  has  already  been  pointed  out,  the  vapor  approaching 
the  compressor  may  be  treated  as  though  it  were  dry  and 
saturated,  each  pound  having  the  total  heat  A2.  The  vapor 
discharged  by  the  compressor  at  the  temperature  ts  and  the 
pressure  pl  will  have  the  heat 


The  heat  added  to  each  pound  of  fluid  by  the  compressor  is 
consequently 


and    an   approximate   calculation    of   the   horse-power  of  the 
compressor  may  be  made  by  the  equation 


4i 

or,  substituting  for  M  from  equation  '       N 


„ 


33ooo(A,  - 


The  power  thus  calculated  must  be  multiplied  by  a  factor 
to  be  found  by  experiment  in  order  to  find  the  actual  power 
of  the  compressor.  Allowance  must  be  made  for  friction  to 
find  the  indicated  power  of  the  steam-engine  which  drives  the 
motor;  for  this  purpose  it  will  be  sufficient  to  add  ten  or  fif- 
teen per  cent  of  the  power  of  the  compressor. 

The  heat  in  the  fluid  discharged  by  compressor  is  equal  to 
the  sum  of  the  heat  brought  from  the  vaporizing-coils  and  the 


REFRIGERA  TING-  MA  CHINES.  493 

heat  equivalent  of  the  work  of  the  compressor.  The  heat 
that  must  be  carried  away  by  the  cooling  water  per  minute  is 
consequently 

0,  =  M(\  -  <?,)  +  M\ct(t,  -  O  +  A,  _  A,  ; 
.'.    Q,  =  MMt.-t,)  +  rl},  .......     (376) 

where  rl  is  the  heat  of  vaporization  at  the  pressure  /r 

If  the  cooling  water  has  the  initial  temperature  tt  and  the 
final  temperature  tk,  and  if  9t  and  yk  are  the  corresponding 
heats  of  the  liquid  for  water,  then  the  weight  of  cooling 
water  used  per  minute  will  be 


G  =          •  >  .....     (377) 

^k   -    *< 

If  the  vapor  at  the  beginning  of  compression  can  be  as- 
sumed to  be  dry  and  saturated,  then  the  volume  of  the  piston 
displacement  of  a  compressor  without  clearance,  and  making 
N  strokes  per  minute,  is 


(378) 


To  allow  for  clearance,   the  volume  thus  found  may  be 
divided  by  the  factor 


m\pj         m 

as  is  explained  on  page  447.  The  volume  thus  found  is  further 
to  be  multiplied  by  a  factor  to  allow  for  inaccuracies  and 
imperfections. 

The  vapors  used  in  compression-machines  are  liable  to  be 
mingled  with  air  or  moisture,  and  in  such  case  the  performance 
of  the  machine  is  impaired.  To  allow  for  such  action  the  size 
and  power  of  the  machine  must  be  increased  in  practice  above 


494  THE  R  MOD  YNAMJCS    OF   THE   STEAM-ENGINE.  . 

those  given   by  calculation.     Proper  precautions  ought  to  be 
taken  to  prevent  such  action  from  becoming  of  importance. 

Calculation  for  a  Compression  Refrigerating-machine.— 
Let  it  be  required  to  find  the  dimensions  and  power  for  an 
ammonia  refrigerating-machine  to  produce  2000  pounds  of  ice 
per  hour  from  water  at  80°  F.  Let  the  temperature  of  the 
brine  in  the  freezing-tank  be  15°  F.,  and  the  temperature  in 
the  condenser  be  85°  F.  Assume  that  the  machine  will  have 
one  double-acting  compressor,  and  that  it  will  make  80  revolu- 
tions per  minute. 

The  heat  of  the  liquid  at  80°  F.  is  48.09  B.  T.  u.,  and  the 
heat  of  liquefaction  of  ice  is  144,  so  that  the  heat  which  must 
be  withdrawn  to  cool  and  freeze  one  pound  of  water  will  be 

48.09  -)-  144.=  192.09  B.  T.  u. 

If  we  allow  50  per  cent  loss  for  radiation,  conduction,  and 
melting  the  ice  from  the  freezing-cans,  the  heat  which  the 
machine  must  withdraw  for  each  pound  of  ice  will  be  about 
300  B.  T.  U.  ;  consequently  the  capacity  of  the  machine  will 
be 

Ql  =  2000  X  300  -f-  60  =  i  oooo  B.  T.  u.  per  minute. 

The  pressures  corresponding  to  15°  and  85°  F.  are  42.43 
and  165.47  pounds  absolute  per  square  inch,  so  that  by  equa- 
tion (374) 

'  =«*•*• 


.-.  /,  =  668.5  —460.7  ^207°.8  F. 
The-horse-power  of  the  compressor  is 


< 

33000(A,2  -  9l) 

778  x  i  oooojo.  50836(207.  8  —  85)4-556  —  535J 

33000(535  -58)  -41'2' 


REFRIGERA  TING-MA  CHINES. 


495 


If  we  allow  10  per  cent  for  imperfections  the  compressor 
will  require  45  horse-power.  If  further  15  per  cent  is  allowed 
for  friction  the  steam-engine  must  develop  53  horse-power. 

From  equation  (374)  the  weight  of  ammonia  used  per 
minute  is 

M=  Q,  -=-  (\  —  <ff)  =  i oooo -=-(535  —  58)  =  21  pounds; 


t 


and   by   equation  (3/8)  the  piston  displacement  for  the  com- 
pressor will  be 

21  X  6.93 


N 


2  X  80 


=  0.91  cubic  feet. 


If  ten  per  cent  is  allowed  for  clearance  and  imperfect  valve 
action  the  piston  displacement  will  be  one  cubic  foot,  and  the 
diameter  may  be  made  ioj  inches  and  the  stroke  20  inches. 

Fluids  Available. — The  fluids  that  have  been  used  in 
compression  refrigerating-machines  are  ether,  sulphurous  acid, 
ammonia,  and  a  mixture  of  sulphurous  acid  and  carbonic  acid, 
known  as  Pictet's  fluid.  The  pressures  of  the  vapors  of  these 
fluids  at  several  temperatures,  and  also  the  pressure  of  the 
vapors  of  methylic  ether  and  carbonic  acid,  are  given  in  the 
following  table : 

PRESSURES    OF   VAPORS,  MM.   OF   MERCURY. 


Temperatures, 
degrees 
Centigrade. 

Ether. 

Sulphur 
Dioxide. 

Methyl- 
ether. 

Ammonia. 

Carbon 
Dioxide. 

Pictet's 
Fluid. 

—  30 

287.  s. 

576.  =; 

866.1 

*8< 

—  20 
—  10 
0 
10 
20 
30 
4O 

68.9 
114  7 
184.4 
286.8 
432.8 
634.8 
QO7.O 

479-5 
762.5 
1165.1 
1719.6 
2462  .  i 
3431-8 

467O   2 

882.0 
1306.6 
1879.0 
2629.0 
3586.0 
4778.0 

1392.1 
2144.6 
3183.3 
4574-0 
6387-8 
8701.0 

IJCQC    a 

15142 
20340 
26907 
34999 
44717 
56119 
60184. 

745 
1018 

1391 
1938 

2584 
3382 

A'lA'J 



Ether  was  used  in  the  early  compression-machines,  but  at 
the  temperatures  maintained  in  the  refrigerator  the  pressure  is 
small  and  the  specific  volume  large,  so  that  the  machines,  like 
air  refrigerating-machines,  were  either  feeble  or  bulky.  More- 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

over,  air  was  liable  to  leak  into  the  machine  and  unduly  heat  the 
compressor  cylinder.  Sulphur  dioxide  has  been  used  success- 
fully, but  it  has  the  disadvantage  that  sulphuric  acid  may  be 
formed  by  the  leakage  of  moisture  into  the  machine,  in  which 
case  rapid  corrosion  occurs.  Ammonia  has  been  extensively 
used  in  the  more  recent  machines  with  good  results.  When 
distilled  from  an  aqueous  solution  it  is  liable  to  contain  con- 
siderable moisture.  As  is  shown  by  the  table,  Pictet's  fluid 
has  a  pressure  at  low  temperature  intermediate  between  the 
pressures  of  sulphur  dioxide  and  ammonia,  and  the  pressure 
increases  slowly  with  the  temperature.  It  has  been  used  by 
the  inventor  only,  and  does  not  appear  in  practice  to  have  any 
advantage  over  ammonia. 

Absorption  Refrigerating  Apparatus.— Fig.  96  gives  an 
ideal  diagram  of  a  continuous  absorption  refrigerating  appara- 
tus. It  consists  of  the  following  essential  parts:  (i)  the 
generator  B,  containing  a  concentrated  solution  of  ammonia 
in  water,  from  which  the  ammonia  is  driven  by  heat;  (2)  the 
condenser  C,  consisting  of  a  coil  of  pipe  in  a  tank,  through 
which  cold  water  is  circulated ;  (3)  the  valve  V,  for  regulating 
the  pressures  in  C  and  in  /;  (4)  the  refrigerator  /,  consisting 
of  a  coil  of  pipe  in  a  tank  containing  a  non-freezing  salt  solu- 
tion ;  (5)  the  absorber  A,  containing  a  dilute  solution  of 
ammonia,  in  which  the  vapor  of  ammonia  is  absorbed ;  and 
(6)  the  pump  P  for  transferring  the  solution  from  the  bottom 
of  A  to  the  top  of  B\  there  is  also  a  pipe  connecting  the  bot- 
tom of  B  with  the  top  of  A.  It  is  apparent  that  the  condenser 
and  refrigerator  or  vaporizer  correspond  to  the  parts  B  and  C 
of  Fig.  95,  and  that  the  absorber  and  generator  take  the  place 
of  the  compressor.  The  pipes  connecting  A  and  B  are 
arranged  to  take  the  most  concentrated  solution  from  A  to 
B,  and  to  return  the  solution  from  which  the  ammonia  has 
been  driven,  from  B  to  A.  In  practice  the  generator  B  is 
placed  over  a  furnace,  or  is  heated  by  a  coil  of  steam-pipe,  to 
drive  off  the  ammonia.  Also,  arrangements  are  made  for 
transferring  heat  from  the  hot  liquid  flowing  from  £  to  A  to 


RE  FRIG  ERA  TING-MA  CHINES. 


497 


the  cold  liquid  flowing  from  A  to  B.  As  the  ammonia  is  dis- 
tilled from  water  in  B  the  vapor  driven  off  contains  some 
moisture,  which  causes  an  unavoidable  loss  of  efficiency. 

The  earliest  absorption  apparatus,  made  by  Carre,  con- 
sisted of  a  cylindrical  receptacle  containing  a  solution  of 
ammonia,  and  acting  alternately  as  generator  and  absorber,  in 
open  communication  through  a  pipe  with  a  vessel  of  double 


FIG.  96. 

conical  form,  acting  alternately  as  condenser  and  refrigerator. 
In  use,  the  generator  was  placed  on  a  furnace  and  the  con- 
denser in  a  tank  of  cold  water,  and  the  ammonia  driven  off 
from  the  solution  condensed  between  the  inner  and  outer 
conical  surfaces  of  the  condenser.  When  a  sufficient  amount 
of  liquid  ammonia  had  collected,  the  vessel  containing  the 
solution  was  transferred  from  the  furnace  to  the  cold-water 
tank,  and  became  thereby  changed  into  the  absorber.  The 
condenser  at  the  same  time  became  the  vaporizer  or  refriger- 
ator, and  after  receiving  a  mould  containing  water  to  be  frozen, 
was  securely  wrapped  with  non-conducting  material.  Appa- 
ratus of  this  kind  is  only  fitted  for  work  on  a  small  scale,  and 
is  inefficient. 

An  adaptation  of  Carry's  apparatus  has  been  used  in  re- 
frigerator-cars for  carrying  perishable  freight.  In  the  car  are 
placed  two  receptacles — one  containing  liquid  ammonia,  which 
maintains  a  low  temperature  by  vaporization ;  and  the  other 


498  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

containing  water,  to  absorb  the  ammonia  as  it  formed.  At 
the  end  of  the  route,  or  when  necessary,  the  receptacles  are  re- 
charged— one  with  liquid  ammonia  and  the  other  with  fresh 
water.  The  ammonia  in  the  rejected  solution  is  regained  by 
distillation. 

Vacuum  Refrigerating  Apparatus. — A  form  of  absorption 
apparatus  uses  water  for  the  volatile  liq.uid  and  concentrated 
sulphuric  acid  for  the  absorbent.  From  the  fact  that  vapor  of 
water  at  freezing-point  has  a  very  low  tension  such  apparatus 
are  called  vacuum  apparatus. 

The  first  apparatus  of  this  kind  was  designed  for  freezing 
water  in  carafes,  and  consisted  of  a  good  air-pump  and  a  re- 
ceptacle containing  oil  of  vitriol.  The  carafe,  well  wrapped  in 
non-conductor,  was  attached  to  a  pipe  leading  to  the  sulphuric- 
acid  receptacle,  the  pump  was  worked  till  a  good  vacuum  was 
produced,  and  the  acid  was  stirred  to  present  fresh  acid  to  the 
vapor  which  rapidly  streamed  from  the  water  at  the  low  pres- 
sure produced.  The  vaporization  of  about  one-sixth  of  the 
weight  of  the  water  was  found  to  be  sufficient  to  freeze  the 
remainder. 

An  ideal  sketch  of  a  continuous  vacuum  apparatus  is  shown 
by  Fig.  97.  At  B  is  an  air-pump  capable  of  producing  a 
vacuum  of  one  or  two  mm.  of  mercury  in  the  chamber  AC. 
At  //there  is  a  tank  of  concentrated  sulphuric  acid,  from  which 
a  spray  is  delivered  at  J.  The  acid  absorbs  the  vapor  found 
in  the  chamber  at  the  low  pressure  existing  there,  gathers  in 
the  tank  y,  and  flows  out  through  the  pipe  A",  which  is  of  suf- 
ficient length  to  deliver  the  acid  against  atmospheric  pressure 
in  the  tank  L.  The  dilute  acid  is  reconcentrated  and  returned 
to  the  tank  H.  At  G  is  a  pipe  supplying  fresh  water  which 
passes  through  the  water-injector  s  and  throws  a  jet  of  salt 
solution  into  the  chamber  at  A.  The  finely  divided  jet  loses 
fresh  water  by  vaporization,  is  chilled,  and  gathers  in  the  bot- 
tom of  the  chamber.  The  salt  solution  flows  through  the  pipe 
F  in  the  cold-chamber  EE,  taking  up  heat  on  the  way,  and  is 
again  thrown  into  the  chamber  with  a  fresh  supply  of  water 


REFRIGERA  TING -MA  CHINES. 


499 


from  the  pipe  G.     At  A^and  TV  are  screens  to  prevent  splash- 
ing of  water  into  the  upper  part  of  the  chamber. 


FIG.  97. 

Tests  of  an  Air  Refrigeratiag-machine. — An  air  refriger- 
ating-machine,  constructed  under  the  Bell-Coleman  patent, 
was  tested  by  Professor  Schroter*  at  an  abattoir  in  Hamburg, 
where  it  was  used  to  maintain  a  low  temperature  in  a  storage- 
room.  The  machine  is  horizontal,  and  has  the  pistons  for  the 
expansion-  and  compression-cylinders  on  one  piston-rod,  the 
expansion-cylinder  being  nearer  the  crank.  Power  is  furnished 
by  a  steam-engine  acting  on  a  crank  at  the  other  end  of  the 
main  shaft  and  at  right  angles  to  the  crank  driving  the  air- 
pistons.  Both  the  steam-cylinder  and  the  expansion-cylinder 
have  distribution  slide-valves,  with  independent  cut-off  valves. 
The  main  dimensions  are  given  in  the  following  table : 

*  Untersuchungen  an  Kaltemachinen,  1887. 


5oo 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


DIMENSIONS    BELL-COLEMAN  MACHINE. 


Steam 
Cylinder. 

Compression 
Cylinder. 

Expansion 
Cylinder. 

Head 
end. 

Crank 
end. 

Head 
end. 

Crank 
end. 

Head 
end. 

Crank 
end. 

f\ 

0.605 
5-9 

*1 

0.605 

5-8 

71 
9.0 

0.605 
1.4 

71 
6.8 
0.605 
1.4 

53 

9-° 

0.605 
8.9 

53 
9.0 
0.605 
8.9 

"        "  piston-rod,  cm  

Clearance,  per  cent  of  piston  displacement. 

Water  is  sprayed  into  the  compression-cylinder,  and  the 
air  is  further  cooled  by  passing  through  an  apparatus  resem- 
bling a  steam-engine  jet-condenser,  after  which  it  is  dried  by 
passing  it  through  a  system  of  pipes  in  the  cold-room  before 
it  passes  to  the  expansion-cylinder. 

In  the  tests  indicators  were  attached  to  each  end  of  the 
several  cylinders,  and  the  temperature  of  the  air  was  taken  at 
entrance  to  and  exit  from  each  of  the  air-cylinders.  Speci- 
mens of  the  indicator-diagrams  from  the  air-cylinders  show 
for  the  compressor  a  slight  reduction  of  pressure  during  ad- 
mission and  some  irregularity  during  expulsion,  and  for  the 
expansion-cylinder  a  little  wire-drawing  at  cut-off,  and  a  good 
expansion  and  compression,  though  neither  is  complete.  No 
attempt  was  made  to  measure  the  amount  and  temperatures 
of  the  cooling  water. 

The  data  and  results  of  the  tests  and  the  calculations  are 
given  in  Table  LI. 

Tests  of  Compression-machines. — In  Table  LII  are  given 
the  data  and  results  of  tests  on  three  refrigerating-machines 
.on  the  Linde  system  using  ammonia,  and  of  a  machine  on 
Pictet's  system  using  Pictet's  fluid,  all  by  Professor  Schroter. 
The  tests  on  machines  used  for  making  ice  were  necessarily  of 
considerable  length,  but  the  tests  on  machines  used  for  cool- 
ing liquids  were  of  shorter  duration. 

The  cooling  water  when  measured  was  gauged  on  a  weir  or 
through  an  orifice.  In  the  tests  3  to  6  on  a  machine  used  for 
cooling  fresh  water  the  heat  withdrawn  was  determined  by 


REFRIG ERA  TING-MA  CHINES. 

TABLE    LI. 

TESTS    ON    BELL-COLEMAN    MACHINE. 


501 


Number  of  Test  

I 

II 

in 

6 

i  67 

61  2 

61  '? 

Temperatures  of  air,  degrees  Centigrade: 
At  entrance  to  compression  cylinder  

26  8 

At  entrance  to  expansion             "       

19.0 

16.6 

At  exit  from                                  "       

—  47  o 

Mean  effective  pressure,  kgs.  per  sq.  cm.: 

^6 

crank  end  

861 

i  870 

i  860 

82- 

*2 

-go 

x  626 

crank  end     

i  615 

Indicated  horse-power: 

128  85 

Il8      T^ 

Mean  pressure  during  expulsion  from  compression  cylinder,.kgs. 
Mean  pressure  during  admission  to  expansion  cylinder,  kgs..  .. 

3-35 
2.82 

3-25 
2.83 

3.40 
2.84 

Calculation  from  compression  diagram: 
Absolute  pressure  at  end  of  stroke,  kgs  
Absolute  pressure  at  opening  of  admission-valve,  kg.  : 
Head  end          

1.04 
o-?83 

1.04 

o  788 

1.04 

o  764 

Volume  at  admission,  per  cent  of  piston  displacement: 

6  is 

8  so 

8  41 

Weight  of  air  discharged  per  stroke,  kg.: 
Headend                         

Calculation  from  expansion  diagram: 
Absolute  pressure  at  release,  kgs.: 

I'll 

Absolute  pressure  at  compression,  kgs.: 
Head  end                     

Crank  end  ,  

i.  20 

1.  19 

I  .22 

Volume  at  release,  per  cent  of  p.  d.: 
Head  end              

104  65 

104  8 

1^63 

Volume  at  compression,  per  cent  of  p.  d.: 
Headend                   

16  s 

16  6 

10  8 

20   6 

Air  used  per  stroke,  kg.: 

o  278 

Difference  of  weights,  calculated  by  compression  and  expan- 

ii  6 

Elevation  of  temperature  at  constant  pressure,  degrees  Centi- 

66  i. 

64  q 

66  i 

767 

taking  the  temperatures  of  the  water  cooled,  and  by  gauging 
the  flow  through  an  orifice,  for  which  the  coefficient  of  flow 
was  determined  by  direct  experiment.  The  heat  withdrawn  in 
the  tests  7  and  8  was  estimated  by  comparison  with  the  tests 
3  to  6.  The  net  production  of  ice  in  the  tests  i  and  2  was 


502 


THERMODYNAMICS   OF   THE   STEAM-ENGINE. 


TABLE  LII. 

TESTS  ON  COMPRESSION  REFRIGERATING-MACHINES. 

By  Professor  SCHROTER,  Untersuchungen  an  Kciltemaschinen. 

Mean  eftective 
pressure  com- 
pressor, kgs.  pei 
sq.  cm. 

•P»*»O 

itnsin?m 

•pua  PBaH 

•     4-10       in       10       in     ro    -4-     M      M     M     w" 

•jossaad 
-moo  'ainuira  jad  suoiinjoAa^ 

OOOOt^         M          M         VOw'oONlxlOO 

•japUIjAo  U1H31S 

jo  jaMod-asjoq  paiBOipuj 

VO       M                                   .            .       IH       10      N       10      P) 

Mean  effective 
pressure.  Steam 
cylinder,  kgs.  per 
sq.  cm. 

•— 

?  "    :           :     :    :    :  "   t  ^ 

•pua  pB3H 

ro      •*                                  .            ...       ON    00       M 
d       CS         •                                      •••««!« 

•aui3ua 
tuBais  'ajnuira  -»ad  suorjnjoAa^i 

o    o 

-^  ;;::;;  $322 

•?saj  jo  uoiTEjriQ 

B5 

IVl  *^a!lV|f| 

Dimensions  of  the  com- 
pression cylinder. 

•ram  '3310455 

»•;  t,  ,-...  t,,-; 

•rara 
'poj-aojsid  jo  aaiaraBiQ 

•rara  'uojstd  jo  jajaureiQ 

ir>            0                                                    0 

Dimensions  of  the  steam 
cylinder. 

•rara  'ajjoaig 

8=J=     =     =    J,    I,,, 

•rara 
*poj-uo;sid  jo  jaiamBiQ 

I'-  i   ;  i   j  a=  sr  =  = 

•mm  'uojsid  jo  ja^araBiQ 

f=  1=  =  .&.  i... 

_„„ 

ri,     -S                      g       ti 
•5     «  •                    1  ^    'S 

^    c5               u 

•auiqoBra  aqi  jo  raajs^s 

|,  ,  =  r  *.«*|>>;* 

•49qranN 

1H9I09       -^       0       <0    r»    00    Ci    O    T-    *l 

REFRIGERA  TING-MACHINES. 


503 


Heat  withdrawn 

•jnoq  J3d  jdMod 
.        -asjoq  josssjdraoo  jsj 

•+OO      r»      M       f~.    •*  so     f    10   oo    oo 

i 
unoq 

J3d  UMBJpq}IM  }E3H 

fiifiiiiilli 

JO  3imT?J3dUI3J,| 

» 
i-o 

>- 

^•pp                  •''f^'SS'p^ 

!  °  i 

: 

rr=  "  =  n^'p^s^^ 

Ice  produced  per  hour. 

'jau  'jnoq  jsd  uaMod 
-3SJoq  JossajdmoD  jsj 

•      M       1          I         •          •        •        •      10     ri      10    oo' 

•SO113J 

'ssojJS  'jnoq  jsd  lJ3A\6d 
-3SJoq  JOSSsadcaoD  J3<j 

•    oo       oo     O     M    vo 

:   ^    •      1     :     j    •       ^g  jj>  «   g 

•SOJIJJ 

'jnoq  J3d  iDnpojd  53^4 

ro    vO        Ov    \O      N      M 

§  2  1     :     1     i    1      "  ?  E>  ? 

'jnoq  J3d  iDnpojd  ssbjf) 

oo      10      •          ;          ;                              oo      jo    oo      10 

•3  S33Jxtap  'paiiddns 

J31BM  JO  3jniBJ3dai3X 

i  2  :     :     :     :    :       d  H  n 

2 

C8 

bo 

c 

1 

O 

•jnoq 

J3d  XH.WB  P3IJJB3  1?3H 

M-;|  ;  Hi!!!! 

,mm*»m 

VOOO          •*         O       w       10               10O 

•3jm?j3dai3i  repiui 

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504 


THERMODYNAMICS   OF   THE    STEAM-ENGINE. 


determined  directly ;  and  in  the  test  2  the  loss  from  melting 
during  the  removal  from  the  moulds  was  found  by  direct  ex- 
periment to  be  8.45  per  cent.  By  comparison  with  this  the 
loss  by  melting  in  the  first  test  was  estimated  to  be  7.7  per 
cent.  The  gross  production  of  ice  in  the  refrigerator  was  cal- 
culated from  the  net  production  by  aid  of  these  figures.  In  the 
tests  9  to  12  on  the  Pictet  machine  the  gross  production  was 
determined  from  the  weight  of  water  supplied,  and  the  net 
production  from  the  weight  of  ice  withdrawn. 

A  separate  experiment  on  the  machine  used  for  cooling 
brine  gave  the  following  results  for  the  distribution  of  power: 

Total  horse-power 57. 1 

Power  expended  on  compressor 19.5 

"               "           "    centrifugal  pump 9.8 

"               "           "    water-pump 3.6 

The  centrifugal  pump  was  used  for  circulating  the  brine 
through  a  system  of  pipes  used  for  cooling  a  cellar  of  a  brew- 
ery. The  water-pump  supplied  cooling  water  to  the  con- 
denser and  for  other  purposes. 

A  similar  test  on  the  Pictet  machine  gave : 

Power  of  engine  alone  . .  , 7.9  H.  P. 

"       "        "       and  intermediate  gear 16.6 

"       "        "       gear,  and  pump 20.0 

From  the  above  data  the  following  table  was  arranged  for 
the  several  tests  on  this  machine : 

INDICATED  AND  EFFECTIVE  WORK. 

Number  of  Test.  9  10  11  12 

Indicated  work  without  compressor — 19.9  20.0  20.0  19.9 

14    engine  alone 7.9  8.0           7.9  7.9 

Effective  work  of  steam-engine 77.1  80. i  84.6  94.4 

Indicated  work  of  steam-engine 91.2  94.5  99.2  109.8 

Mechanical  efficiency  of  steax-engine 0.84  0.85  085  0.85 

Power  absorbed  by  intermediate  gearing ..11.2  11.2  11.2  11.2 

Power  absorbed  by  compressor 65. g(?)  68.9  73.4  83.2 

Indicated  power  of  compressor. ..'. 52.0  61.7  66.4  75.0 

Mechanical  efficiency  of  compressor o.79(?)  0.89  0.90  0.90 


REFR1GERA  TING-MA  CHINES. 


505 


In  1888  comparative  tests  were  made  by  Professor  Schro- 
ter  on  3.  Linde  and  on  a  Pictet  refrigerating-machine,  in  a 
special  building  provided  by  the  Linde  Company  which  had 
every  convenience  and  facility  for  exact  work.  The  following 
table  gives  the  principal  dimensions  of  the  machines: 

PRINCIPAL   DIMENSIONS    OF    LINDE    AND     PICTET 
REFRIGERATING-MACHINES. 


Linde. 

Pictet. 

j^'bo 

J1  -°J 

nQ     f. 

25  .03 

4gc 

Stroke  of  steam-piston    cm      

•  J 

Aa 

/u 

ff> 

Diameter  of  pipe  in  vaporizers,  external,  mm.  .  .  . 
do.                             internal,  mm.  ... 

42 

40.5 
32 

44 
36 

33U-  5 

eeS    c 

D  jo-^ 
C«fi     o 

Diameter  of  pipe  in  condenser,  external,  mm.  .  .  . 
do.                            internal,  mm  

:>:>0o 
38.5 
30 

c  eft    2 

3j°-  • 

44 
36 

j.8^   i 

The  Linde  machine  used  ammonia  and  was  allowed  to 
draw  a  mixture  of  liquid  and  vapor  into  the  compressor,  so 
that  no  water-jacket  was  required.  The  Pictet  machine  used 
Pictet's  fluid  and  had  the  compressor  cooled  by  a  water-jacket. 

The  data  and  results  of  the  tests  are  given  in  Tables  LIII 
and  LIV.  Five  tests  on  each  machine  were  made  with  only 
one  of  the  two  vaporizers  in  use,  and  three  were  made  with 
both  in  use.  The  temperature  of  the  salt  solution  or  brine, 
from  which  heat  was  withdrawn  by  the  vaporizers,  was  allowed 
to  vary  about  three  degrees  centigrade  from  entrance  to  exit. 
The  entrance  temperatures  were  intended  to  be  6°  C.,  —  2°  C., 
—  10°  C.,  and  —  18°  C.  The  cooling  water  was  supplied  to 
the  condenser  at  about  9°.  5  C.  for  all  tests,  and  for  all  but 
one  it  left  the  condenser  with  a  temperature  of  nearly  20°  C. ; 
the  fifth  test  on  each  machine  was  made  with  the  exit  tem- 
perature of  the  cooling  water  at  about  35°  C. 


506 


THERMOD  YNAM1CS   OF   THE   STEAM-ENGINE. 


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By  Professor  M. 

Steam-engine: 
Revolutions  per  minute  
Horse-power  
Compressor: 

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REFRIGERA  TING- MA  CHINES. 


507 


By  Professor  M.  SCHROTER,  Vergleichende  Versuche  an  Kiiltemaschinen. 

Two  vaporizers. 

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W         U                     >                                              U 

5O8  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

The  pressure  in  the  compressor  depended,  of  course,  on 
the  temperatures  of  the  brine  and  the  cooling-water.  For  all 
the  tests  except  the  fifth  on  each  machine,  the  maximum 
pressure  of  the  working  substance  was  nearly  constant :  about 
9  kilograms  per  square  centimetre  for  ammonia  and  about  4 
kilograms  for  Pectet's  fluid.  The  fifth  test  had  considerably 
higher  pressure,  corresponding  to  the  higher  temperature  in 
the  condenser.  The  minimum  pressure  of  the  working  sub- 
stance of  course  diminished  as  the  brine  temperature  fell. 

The1  heat  yielded  per  hour  to  the  ammonia  in  the  vapor- 
izer was  calcul-ated  by  multiplying  together  the  amount  of 
brine  used  in  an  hour,  the  specific  heat  of  the  brine,  and  its 
increase  of  temperature.  But  the  initial  and  final  tempera- 
tures were  not  quite  constant,  and  so  a  correction  was  ap- 
plied as  indicated  in  the  tables.  The  heat  abstracted  from  the 
ammonia  in  the  condenser  was  calculated  from  the  water  used 
per  hour  and  its  increase  of  temperature.  The  calculation 
for  Pectet's  machine  involves  also  the  jacket-water  and  its  in- 
crease of  temperature.  A  correction  is  applied  for  the  varia- 
tions of  initial  and  final  temperatures  of  the  cooling-water. 
If  the  heat  equivalent  of  the  work  of  the  compressor  is  added 
to  the  heat  yielded  by  the  vaporizer  the  sum  should  be  equal 
to  the  heat  abstracted  by  the  cooling-water.  The  per  cent 
of  difference  between  these  two  calculations  of  the  heat  ab- 
stracted by  the  cooling-water  is  a  measure  of  the  accuracy  of 
the  tests. 

The  refrigerative  effect  is  obtained  by  dividing  the  heat 
yielded  by  the  vaporizer  by  the  horse-power  of  the  steam-cyl- 
inder. The  first  four  tests  with  constant  temperature  in  the 
condenser  show  a  regular  decrease  in  the  refrigerative  effect 
for  each  machine  as  the  temperature  of  the  brine  and  the 
minimum  pressure  of  the  working  substance  is  reduced.  The 
three  tests  with  the  entire  vaporizing  surface  in  use  show  a 
like  result.  The  fifth  test,  with  a  higher  temperature  in  the 
condenser,  shows  a  less  refrigerative  effect  than  the  second  test, 
which  has  nearly  the  same  brine  temperatures.  These  results 


REFRIGERA  TING-MA  CHINES. 


509 


are  in  concordance  with  the  idea  that  a  refrigerating-machine 
is  a  reversed  heat-engine ;  for  a  heat-engine  will  have  a  higher 
efficiency  and  will  use  less  heat  per  horse-power  when  the 
range  of  temperatures  is  increased,  and  per  contra,  a  refriger- 
ating-machine will  be  able  to  transfer  less  heat  per  horse- 
power as  the  range  of  temperatures  is  increased. 

Table  LV  gives  the  data  and  results  of  tests  made  by 
Professor  Denton  on  an  ammonia  refrigerating-machine.  The 
only  items  requiring  explanation  are  the  refrigerative  effect 


TABLE  LV. 

TESTS    ON    AMMONIA    REFRIGERATING-MACHINE. 
By  Professor  J.  E.  DENTON,   Trans.  Am.  Soc.  Mech.  Engr.,  vol.  xii,  p.  326. 


i 

ii 

III 

IV 

Pressure  above  atmosphere,  pounds  per  square  inch: 
Ammonia  from  compressor.  ...                                   

161 

28 

8    2 

Temperature,  degrees  Fahrenheit: 

36  76 

6    27 

do      outlet....                

28.86 

;6  6c 

8^  66 

3c  A 

8,46 

82  86 

44.  6q 

<6  7 

do.             entering  compressor  

39 

£ 

10.13 

34 

do.                            do.                 calculated  
do              entering1  condenser                

229 

£ 
200 

237 

1  68 

228l 

Specific  gravity.  .         .  .             

O.82 

0.78 

o  78 

o  78^ 

u  68 

16  67 

do                      from  compressor  displacement. 

Heat  account,  B.  T.  u.  per  minute: 
Given  to  ammonia  by  brine  
do                    compressor               .     .         

14776 
27860 

7i876 

8824 
2518 

14647 

16? 

Taken  from  ammonia  by  condenser          .... 

608 

6-6 

406 

do.                      atmosphere  

182 

778 

18032 

10816 

18017 

Power,  etc.: 
Revolutions  per  minute        .... 

"?8  oq 

57  88 

58.80 

8s  o 

7,  g 

88  6 

2 

0.1, 

o  83 

0.86 

o  8^ 

Refrigerative  effect  : 
Tons  of  ice  (melted)  in  24  hours.  
B.  T.  U.  abstracted  from  brine  per  horse-power,  minutes 

74.8 
174 

36.43 
197 

44.64 
197 

74-56 
i96 

$10  THERMODYNAMICS   OF   THE   STEAM-ENGINE. 

and  the  calculated  temperature  of  the  vapor  leaving  the  con- 
denser; the  latter  was  calculated  by  the  equation 


and  shows  both  the  cooling  effect  of  the  jacket  and  the  error 
in  assuming  an  adiabatic  compression.  The  refrigerative  ef- 
fect was  obtained  by  dividing  the  B.T.U.  given  to  the  am- 
monia in  a  minute  by  the  horse-power  of  the  steam-cylinder. 
The  tons  per  horse-power  in  24  hours  was  obtained  by  multi- 
plying the  refrigerative  effect  in  thermal  units  per  minute  by 
the  number  of  minutes  in  a  day  and  then  dividing  the  product 
by  2000  (the  pounds  in  a  short  ton)  and  by  144  (the  heat  of 
melting  a  pound  of  ice).  The  pounds  of  ice  per  pound  of 
coal  was  based  on  an  assumed  consumption  of  three  pounds 
of  coal  per  horse-power  per  hour,  and  was  calculated  by  mul- 
tiplying the  B.T.U.  per  horse-power  per  minute  by  60  and 
dividing  by  3  X  144. 

The  main  dimensions  of  the  machine  were : 

Diameter  of  ammonia  cylinder  (single-acting) 12  inches. 

Stroke  of  ammonia  cylinder  (single-acting) 30      " 

Diameter  of  steam-cylinder 18      " 

Stroke  of  steam-cylinder 36      " 

Diameter  of  pipe  for  vaporizer  and  condenser I       " 

Length  of  pipe  in  vaporizer 8000  feet. 

do.  condenser, 5000     " 

Test  of  an  Absorption-machine. — The  principal  data 
and  the  results  of  a  test  made  by  Professor  J.  E.  Denton* 
on  an  absorption  ammonia  refrigerating-machine  are  given  in 
Table  LVI.  The  machine  is  applied  to  chill  a  room  of  about 
400,000  cubic  feet  capacity  at  a  pork-packing  establishment 
at  New  Haven,  Conn.  In  connection  with  this  test  the 
specific  heat  of  the  brine,  which  served  as  a  carrier  of  heat 
from  the  cold  room  to  the  ammonia,  was  determined  by  direct 

*  Trans.  Am.  Soc.  Mech.  Eng.,  vol.  x,  May,  1889. 


REFRIGERA  TING-MA  CHINES. 

TABLE    LVI. 

TEST   OF    AN    ABSORPTION-MACHINE. 
SEVEN  DAYS'  CONTINUOUS  TEST,  SEPT.  11-18,  1888. 


Average  pressures 

above  atmosphere     Coo,er 
inlbs.persq.»n.    [Absorber 

Atmosphere  in  vicinity  of  machine 80 

Generator  272° 

R  .        j  Inlet 21.205 

Bnne    1  Outlet 16.16 

Condenser  ^-;V:;;:;V:;:;::::  g* 

Average     tempera-,                     {Inlet.., 80 

tures  in    Fahren-^J  Absorber -j  Qutjet  m 

heit  degrees.                           /  Upper  outlet'to  generator'. ......  212 

Heater  •<  Lower       *'     "absorber 

(  Inlet  from  absorber 

Inlet  from  generator 272 

Water  returned  to  main  boilers  from  steam 

coil 260 

Average    range    oi  I  Condenser 25$ 

temperatures-<  Absorber. . .    31 

Fahr.  degrees.        (Brine - 5.13 

Brine  circulated  per  j  Cubic  feet 1,633.7 

hour.                       \  Pounds ....  119,260 

Specific  heat  of  brine 0.800 

Cooling  capacity  of  machine  in  tons  of  ice  per  day  of  24  hours. .  40.67 
Steam  consumption    per   hour,  to   volatilize    ammonia,  and   to 

operate  ammonia  pump Ibs.  1,986 

T?I-     •     «.  A  f  Per  pound  of  brine 4.104 

Eliminated  j  ^  pef  houf ^^ 

Of  refrigerating  effect  per  pound  of  steam 

consumption 243 

Reierted  \  At  condenser>  Per  hour 918,000 

British    thermal  'a  \  At  absorber  "        1,116,000 

units.  ^  f  On  entering  genera- 

Per  pound  of  Steam     ^^  -^  '•«* 

[      tor  coil 271 

Consumed  by  generator  per  Ib.  of  steam 

condensed 932 

Condensing  water  per  hour,  in  Ibs 36,000 

Equivalent  ice  production   per  pound  of  coal,  if  one   pound  of 

coal  evaporates  ten  pounds  of  steam  at  boiler 17. 1 

Calories,  refrigerating  effect  per  kilogramme  of  steam  consumed.  135 

HEiiE'rE  a 


512  THERMODYMAMICS   OF   THE   STEAM-ENGINE. 

experiment.  The  brine  chilled  and  the  cooling  water  used 
were  measured  with  meters,  which  were  afterwards  tested 
under  the  conditions  of  the  experiment. 

It  is  interesting  to  compare  the  refrigerative  effects  ex- 
pressed in  pounds  of  ice  per  pound  of  coal.  On  this  basis  the 
compression-machine  tested  by  Professor  Denton  has  an  ad- 
vantage of 

24.1  —  17.1 

l          X  100=  19  per  cent. 

But  this  comparison  is  really  unfair  to  the  compression-ma- 
chine, for  its  steam-engine  is  assumed  to  require  a  consump- 
tion of  three  pounds  of  coal  per  horse-power  per  hour,  while 
the  calculation  for  the  absorption-machine  is  based  on  the  as- 
sumption that  a  pound  of  coal  can  evaporate  ten  pounds  of 
water;  but  an  automatic  condensing-engine  of  the  given 
power  should  be  able  to  run  on  20  or  22  pounds  of  steam  per 
horse-power  per  hour. 


INDEX. 


PAGE 

Absolute  temperature 32,  57,  71 

Absorption  refrigerating  apparatus - 496 

Adiai  atic  for  gases 66 

for  liquid  and  vapor 117,  120 

for  superheated  vapor 135 

lines 19 

Air-compression,  efficiency 455 

Air-compressor,  calculation 459 

compound 451 

cooling  during  compression 444 

effect  of  clearance 447 

friction 454 

fluid-piston 443 

moisture  in  cylinder 445 

power  expended 446 

three-stage 452 

Air,  flow  of 154 

friction  in  pipes 463 

pump 457 

thermometer 71 

Alternative  method 49 

Ammonia 145 

Augsburg,  engine  test 356,  357 

Automatic  and  throttle  engines 420 

Automatic-engine,  tests 363,  381,  382 

Bache,  tests  on 388 

Barrel-calorimeter 289 

Bell-Coleman  refrigerating  machine 498 

Boston  Main  Drainage,  engine  test 360 

Boyle's  law ....    54 

British  thermal  unit 7 

Brookline,  tests  on 358 

Callendar  and  Nicolson 343 

Calorie 15 

513 


514  INDEX.    , 

PAGE 

Calorimeter,  barrel 289 

continuous 291 

separating 297 

throttling 294 

Carnot's  engine 25 

function 31 

principle 29 

Characteristic  equation 2 

for  gases 55 

for  superheated  vapors   -  -    126,  130 

Chestnut  Hill,  engine  test 355 

Coal-gas  analysis 210 

Coefficient  of  dilatation 55 

Colchester,  test  on 358 

Compound  air-compressor .' 451 

air-engine 470 

Compound-engine 255 

cross-compound 268 

direct-expansion 263 

gain  from  compounding 413 

indicator  diagrams 262 

low-pressure  cut-off 260 

ratio  of  cylinders :  61 

total  expansions 259 

with  receiver 258 

without  receiver 257 

Compressed-air 442 

effect  of  clearance 447 

interchange  of  heat 449 

storage  of  power 475 

temperature  after  compression 448 

transmission  of  power 474 

Compressed-air  engine 467 

calculation 471 

compound 470 

consumption 468 

final  temperature 468 

interchange  of  heat 469 

moisture  in  cylinder 470 

power  of 467 

volume  of  cylinder 469 

Condensation  in  high-speed  engines 424 

Condensers 249 

cooling  surface 251 

ejector 193 

Cornell,  tests  on  engine 396 


INDEX.  515 


Crensot,  tests  on  engine 381,  382 

Critical  temperature no 

Curve  of  constant  steam  weight in 

Cut-oft  and  expansion 417 

Cycle,  closed 28 

non-reversible 42 

reversible 27 

Dallas,  tests  on 388^ 

Dean 3S9^3&> 

Delafond 381,  382,  435 

Density  of  gases 59 

of  mercury 58 

of  vapors 107 

Denton 361,  400,  509,  510 

Designing  steam-engines 252,  277 

Dexter,  tests  on 388 

Diesel  motor 221 

Differential  coefficient  dp/dt 91 

Dilatation,  coefficient  of 55 

Direct-acting  pumps,  tests 364,  365 

Dixwell's  tests 371 

Dynamometers 284 

Effect  of  raising  steam-pressure 248,  366 

Efficiency 29 

mechanical '. 430 

of  compressed-air  transmission 474 

of  reversible  engines 35 

of  steam-engine 230,  238,  240,  244 

Ejector 192 

condenser 193 

Engine,  Carnot's 25 

compressed-air 467 

Ericsson's 199 

friction  of 429 

gas 194,  200 

hot-air 194 

oil 216 

reversible 27 

steam 229 

Stirling's 196 

Entropy 22 

due  to  evaporization 116 

expression  for 38 

of  a  liquid 115 

of  a  liquid  and  vapor 117 

of  gases 70 


INDEX. 

PACK 

Entropy  of  superheated  vapor. 128 

scale  of 34 

Ericsson's  hot-air  engine 199 

Eutaw,  tests  on «,.......,  369 

Exhaust-steam  injector 186 

Expansion  and  cut-off „ 417 

Exponential  equation 69 

First  law  of  thermodynamics 15 

application  of 44 

application  to  superheated  vapors 125 

application  to  vapors 103 

Flow  of  air,  Fliegner's  equations 154 

in  pipes .    463 

maximum  velocity 155 

through  porous  plug 72 

Flow  of  fluids 149 

of  gases 151 

of  incompressible  fluids 150 

of  saturated  vapor 157 

of  steam,  experiments 159 

of  superheated  vapor 160 

Fluid-piston  compressor 443 

French  and  English  units 57 

Friction  of  engines 429 

distribution 439 

initial  and  load 431 

Fundamental  equations 44 

Fusi  Yama 358 

Gallatin,  tests  on 388 

Gas-engine 200 

governors 220 

ignition 218 

Otto 209 

tests 210,  2i 2,  215 

with  compression  in  cylinder 204 

with  separate  compression 201 

Gas-producers 214 

Gases 54 

adiabatic  equations 66 

density 59 

entropy 70 

flow  of. 151 

general  equations 63 

intrinsic  energy 68 

isoenergic  equation 65 

isothermal  equation 64 


INDEX.  517 

PAGE 

Gases  specific  heats 62 

specific  volumes 59 

Gauges 283 

Gay-Lussac's  law 54 

General  equations  for  gases 63 

for  superheated  vapors 127 

for  vapors 102 

General  principles,  first 2 

second 15 

third 30 

Graphical  representation  of  change  of  energy 20 

of  characteristic  equation 6 

of  efficiency 36 

Gravity,  acceleration  of 57 

Hall's  investigations 341 

Hallauer's  tests 319 

Heat  of  the  liquid 97,  98 

Heat  of  vaporization 100 

Him  engine,  tests  on 320 

Hirn's  analysis 304 

experiments  on  superheated  steam 134 

Hoadley  engine,  tests  on 364 

Holyoke,  tests  on  engine 362 

Hot-air  engines 194 

Indicators 284 

Influence  of  cylinder  walls 301 

Callender  and  Nicolson 343 

Hall 34I 

Hirn's  analysis 304 

Initial  condensation 301 

Injecter 163 

automatic 179 

combining-tube 176 

delivery-tube 176 

double 179 

efficiency  of 177 

exhaust  steam 186 

lifting 178 

Korting 180 

restarting ,  . . .  183 

Schaffer  and  Budenberg 187 

Seller's ' 178 

Seller's  experiments 182,  i£6 

steam-nozzle 175 

tests  on 182,  186,  189 

theory 165 


INDEX. 


Injector  velocity  in  delivery  tube  ......................  .  ..............    17! 

velocity  of  steam-jet  .............  .  ..........................    168 

water  ........  .  .  ..  .  .........................................    I9o 

Interchanges  of  heat,  air-compressors  ...............................   449 

compressed-air-engine.  .  .  .....................  469 

steam-engine  .................................   301 

Intermediate  rcheaters  ..............................................    401 

Internal  latent  heat  of  vapors  .......................................    102 

Intrinsic  energy  ................................  .  ...............  .'  .  .  .      17 

of  gases  ...................................  .........     68 

of  superheated  vapors  ..............................    132 

of  vapors  ...........................................    113 

lona,  tests  on  .......................................................   358 

Isherwood  .........  ......  .  .....................................  363,  370 

Isoenergic  or  isodynamic  line  .......................................      ig 

for  gases  ..............................     65 

V-  for  superheated  vapors  ................   138 

for  vapors  ............................    113 

Isothermal  lines.  ...  ................................................     18 

for  gases  ..........................................     64 

for  superheated  vapors  .............................   138 

for  vapors  .........................................    112 

Joule  and  Thomson's  experiments  ...................................       2 

Joule's  equivalent  ........................................  .  .......    15,  96 

Kennedy  ...........................................................   358 

Kilogram  ...........................................................      57 

Kneass  .............................................................    168 

Laketown  engine  test  ...............................................   399 

Latent  heat  of  expansion  ............................................       g 

Latitude,  standard  .................................................      58 

Laws  of  thermodynamics  ..........................................  15,  30 

application  of  ..............  .............  44,  47 

application  to  gases  ........................     61 

application  to  superheated  vapors  ..........    124 

application  to  vapors  ......................    103 

Leavitt  engines  ........................................  354,  355,  359,  360 

Linde  refrigerating  machine  .........................  „  ..........  502,  506 

Line  of  constant  steam  weight  ......................................    in 

Lines,  adiabatic.  ...  ......................................  19,  66,  117,  135 

isoenergic  ........................................  19,  65,  113,  138 

isothermal.  .  -  .....................................  18,  64,  112.  138 

of  equal  pressure  .....  .  ....................................  18,  112 

of  equal  volume  .............................................      18 

Louisville,  test  on  engine  ...........................................    359 

Marine  engine  tests  ...    ........................................  358,  386 

Mass,  Inst.  Technology,  engine  tests  .......  «  ................  371,  389,  401 


INDEX.  519 

PAGE 

Mechanical  efficiency 430 

Mechanical  equivalent  of  heat 15,  95 

Joule's 96 

Rowland's 95 

Mercury,  density  of 88 

Meteor,  test  on 358 

Meter 88 

Michigan,  tests  on. . . 302 

Miller,  E.  F 355 

Minneapolis,  tests  of  auxiliary  machinery 365 

Natick,  engine  test 360 

New  Bedford,  engine  test ;   361 

Non-reversible  cycles 42 

Oil-engines 216 

Perot's  experiments  on  density  of  vapors 109 

Pictet's  fluid 495 

refrigerating  machine 502,  507 

Porus  plug,  flow  through 72 

Pressure  of  saturated  steam 86,  88 

of  vapors v  80,  90 

specific 3 

Rankine's  equations  for  flow  of  steam 158 

for  pressure  of  steam 89 

Ratio  of  cylinders,  compound  engines 261 

Refrigerating  machines « 479 

absorption 496 

air 480 

calculations,  for 488,  494 

compression 490 

extraction  of  moisture 481 

fluids,  for 495 

proportions 483,  491 

tests 499 

vacuum 498 

Regnault's  equations  for  steam 84 

Relations  of  thermal  capacities 10 

Revenue  steamers,  tests  on 386 

Reversible  cycle <     27 

engine. . 27 

engine,  efficiency 35 

Rontgen's  experiments 76 

Rowland's  experiments 93 

equivalent 95 

reduction  of  air-thermometer 96 

Rush,  tests  on 388 

Saturated  vapors   * 80 


520  INDEX. 


Saturated  vapors  adiabatic  equations 117 

density 107 

entropy 1 16 

flow  of 157 

general  equation 102 

intrinsic  energy 113 

isoenergic  equation 113 

isothermal  equation 112 

pressure  of 86,  88,  91 

specific  heats 105 

specific  volumes 107 

Schmidt's  engines 375 

Schroter's  tests  of  refrigerating  machines 500 

tests  of  steam  engines 357 

Seaton's  multipliers  for  steam-engine  design 253,  278 

Second  law  of  thermodynamics 25 

application  pf 47 

application  to  superheated  vapors  ....    125 

application  to  vapors 104 

Sound, ^velocity  of , 73 

Specific-heat 8 

of  gases 62 

of  liquids -x 98 

of  steam    105 

of  superheated  steam 129,  132 

of  vapors 105 

of  water 97 

Specific-pressure , , 3,  58 

Specific-volume 3 

of  gases 59 

of  liquids 100 

of  vapors 107 

Steam,  curve  of  constant  weight in 

flow  of 157 

pressure  of 86,  88 

Steam-engine 229 

actual 241 

Carnot's  cycle 229 

compound 255 

designing 252,  277 

economy 353 

efficiency 244 

Hirn's  analysis 304,  313,  323,  332,  336 

indicators 284 

influence  of  the  cylinder  walls 301 

leakage  of  valves 350 


INDEX.  521 


Steam-engine  Seaton's  multipliers 253,  278 

steam  jackets 322 

superheated  steam 319 

testing  of 280 

tests  of 353 

triple-expansion 259 

with  non-conducting  cylinder 235 

Steam-jackets 377 

gain  from 400 

Steam-turbine - 425 

Stirling's  hot-air  engine 196 

Storage  of  power,  compressed  air 475 

Sulphur  dioxide 139 

Superheated  vapors 123 

adiabatic  equation 135 

application  of  laws  of  thermodynamics 124 

characteristic  equation 130 

entropy 128 

flow  of 160 

isothermal  line 138 

specific  heat 129,  132 

total  heat 133 

values  of  constants 130 

Temperature 4 

absolute  scale 32 

standard 7 

Temperature-entropy  diagram 37 

Testing  steam-engines 280 

indirect  method 298 

Test  of  blowing-engine 457 

Tests  of  refrigerating  machines,  air 499 

absorption 510 

compression 500 

Tests  of  steam-engines 353 

compound  engines 359,  389,  396 

examples  of  economy 354 

marine  engines 358,  386 

simple  engines 318,  363,  381,  396 

steam-pumps 364,  365 

superheated  steam 368 

triple  engines 355,  389,  396 

Willans's  engine 402 

Thermal  capacities 7 

of  gases 63 

of  superheated  vapors 126 

relations  of 10 


522  INDEX. 

PACK 

Thermal  lines 18 

Thermal  unit 7 

Thermometers 283 

Thomson  and  Joule's  experiments 72 

Thomson's  scale  of  temperature 32 

Throttling  and  automatic  engines 420 

Throttling  calorimeter 294 

Thurston 209,  438 

Total  heat  of  steam 99 

of  superheated  steam 133 

of  vapors 100 

Triple  expansion  engine,  diagrams 273 

Vacuum  refrigerating  apparatus 498 

Value  of  R 60 

Velocity  of  sound 73 

Ville  de  Douvres 358 

Water  injector 190 

Weirs 288 

Willans's  engine 402 

Zeuner's  equations  for  internal  heat no 

Zeuner's  general  equations 51 


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